Praise the sun. Our Dark Souls Walkthrough provides tips for surviving the adventure, a guide to the entire world, and hints for slaying bosses.
Darkroot Garden
From the blacksmith shop in the Undead Parish, you can head down some stairs and pass through a large chamber with a monster. Note that this can be done just about any time you like, as long as you're feeling hearty enough. You don't have to first clear the Undead Parish.
Keep your distance from the monster as you cross the wide chamber. It throws bolts of lightning at you when you are out of its normal range, but you can easily roll out of their way. If you get closer, it can lash out with a far-reaching melee attack or it may try to pounce you. Roll out of the way of either attack and keep going to the opposite end of the chamber.
Once you move past the beast, who you can kill for 1000 souls and the Demon Titanite if you're feeling gutsy, you'll be able to pass through an archway and into the Darkroot Garden area. It's a grassy area deep within the forest. The main enemy you'll encounter here is a walking monstrosity formed from various roots and leaves. It's actually not all that powerful. Fire attacks work well against it, or even moving in close and blocking its swinging roots before using a quick melee attack. The root creature is surprisingly agile and capable of bending to avoid your attacks, so work swiftly.

Head left through the swamp area and you'll encounter several of the beasts. There are glowing points all throughout, but mostly those are just flowers except one point just behind a large boulder (overlooking a ravine to the left where you can see a higher ledge with a corpse and item waiting). You can check the corpse behind the boulder to find a Large Soul of a Nameless Soldier. That's worth snagging.
Near that boulder, there's also a ledge that leads to the right. You'll see an outcropping overlooking a lot of forest. There's a glowing flower near the edge of the ledge. Though it's not easily visible, you can head right from the flower, then circle back left and descend along a path. However, that path leads to a different area known as Darkroot Basin. Keep it in mind but you're not ready to go there just yet.
For now, continue along the main trail past the point where you find the soul of the nameless soldier and you should soon find a glowing point on the wall. It's a moss-covered doorway that you can't pass through unless you have the Crest of Artorias (purchased from the blacksmith in the Undead Parish area for 20,000 souls). Beyond the seal is an extremely lethal area, so you should ignore it for now even if you have the crest. To the left of that sealed doorway, note the brick wall. You can slash at the wall a time or two and destroy it to reveal a hidden ledge with a bonfire waiting. Use that bonfire as you see fit, then turn back the way you came. Near the glowing door, there's a side path.

Follow the side path and you'll find a narrow trail that leads through a defile. Start along it and you'll come to a branch in the path. Along the left route, there's a fog-shrouded door. To the right, you'll see that the trail widens into a clearing. You should approach that clearing cautiously. There's a body with a glowing object waiting for you at the center of the clearing, but it's a trap.
Start into the clearing and when you're ready, loot the corpse to find a Large Soul of a Nameless Soldier. As you grab the item, the ground around you comes to life and three of the root creatures attack you at once. Target one and circle around it so that you can see all of your threats. You need to focus on trying to take them out one at a time, perhaps with fire magic or a firebomb to make things go more smoothly.
When you have eliminated all of the root monsters, head back to the bonfire and use it if you like. Note that this is a great place to farm for souls. Every time you use the bonfire, the monsters in the dead-end clearing regenerate and you can take them down again from just outside the clearing with a flurry of fire spells. Just stay away from them when they lunge or one may grab you and suck life out of you. Each of the moss creatures generate 100 souls, so you can see how easy it would be to build up a lot of souls.

Then when you're done with that exercise, you can go ahead and pass through the mist-shrouded opening. As you start through the clearing, you'll wake a slumbering enemy stone knight. You can't attack him until he stands up. Once he does, you'll find that he's a tough fellow who moves very slowly. He carries a huge sword and a powerful stone greatshield that he may drop if you're fortunate, so steer clear of the weapon and try to strike from the flank or behind. Usually, he'll swing two or three times and then you can move in and get two or three hits in before rolling away to avoid his follow-up. Watch out when he casts a spell, though; you won't be able to roll or move quickly after that until its effects wear off. Fortunately, the spell takes time to cast. You can move in and get in a few hits while he's casting it, potentially allowing you to finish him off before you have to worry about its effects.

Take care of that enemy and continue to explore. Along the edge of the area, you'll find a moss-covered tree that you can attack repeatedly. As you do, notice that it has a life meter. Keep attacking until the tree disappears in blinding light, revealing a hidden path behind it. There are other paths nearby, as well. One leads to a Partisan that you can find on a corpse ahead of a tree, but be careful. The tree has limbs that come to life and can inflict poison, plus one of the vine creatures may follow you and try to attack from the rear.
Grab the weapon and head back out into the main clearing. Note that in this general vicinity, there's a second one of the lumbering giants. Deal with it as you did the first one and head around the area. You'll likely come to a point where there are two of the stone knights sleeping. As they awaken, just run past them and look for a corpse. If you can loot the corpse, you'll find the Elite Knight Helm, the Elite Knight Armor, the Elite Knight Gauntlets and the Elite Knight Leggings. They have terrific defensive properties.

When you're done looting, you can continue exploring and you'll likely find a stone archway where it's possible to enter and fight a boss. You're not done exploring and grabbing items yet, though. For now, return to the place where you hacked apart the tree to reveal a secret path. Head along it and you'll find an enemy that skitters along the ground and looks a bit like a red and black manta ray. It's easily hacked apart, but make sure that you're not being chased by root enemies that will try to hit you from behind if you're not paying attention.

Past that monster, you can find another narrow ravine. Proceed along it and you'll find a spinning tree. You can head around it without contact and then continue through the forest to reach a series of stone steps leading up through a cave. This is a dangerous trail, but one that you need to take. Ascend and watch for another of the stone knights at the top. It will fight you on a narrow ledge. Nearby, there's a corpse you can investigate to obtain the Wolf Ring. You're now on a ledge overlooking the starting point of the stage. There's a bottomless gap ahead of you, though you may be able to leap over it and land on the lower ledge ahead of you, then travel left to return to rest at the bonfire.
Now you're ready to look into fighting the area boss. As a reminder, the route to find him from the bonfire is to head through the area where you passed through the mist, past the sleeping stone knights and toward the back side of the open area they guard. A final stone knight is asleep in front of the doorway you need to enter. Roll past him and then you can climb up some steps in a tower and at the top, you'll be able to pass through the mist and into the area where the boss awaits you.
Moonlight Butterfly
This battle is a slow-paced one and you should have only moderate difficulty winning it if you follow a few simple strategies.
When the Moonlight Butterfly first appears, it is floating slowly to the side of the long bridge where the battle takes place. As it floats in the air, you can't reach it except with projectiles or magic. However, it can hit you. Periodically, it charges up a ball of green light and then it fires a homing shot at your current location. You can roll out of the way to easily avoid it if you have enough stamina. This shot can one-hit kill you, so it's the most important attack to avoid. Sometimes, the butterfly also fires a spread shot or it will fire a laser that sweeps back and forth and tries to find you. Make sure that you roll away from that laser as possible, since it inflicts fairly severe damage. The spread shot will only inflict moderate damage if it hits, so you can withstand that. What's most important is that you dodge the spread shot.

After you dodge its attacks for awhile, the Moonlight Butterfly will be tuckered out. It will stupidly descend to the ledge where you are positioned and will rest there. Rush over to it and hit it with your weapon of choice until it starts to glow. That's a sign that it is about to send a shockwave outward from its location. Quickly back away so that you're not hit by the explosive wave.
The butterfly will now take to the air and the whole process will repeat. If you equip your weapon with two hands to increase the damage it inflicts, you can likely take down the butterfly in only a round or two. It's an easy battle if you know what you're doing.
When you win, you'll receive the Soul of the Moonlight Butterfly. Head along the walkway that it was guarding, then ascend the tower. At the top, you'll find a corpse. Loot it to obtain the Watchtower Basement Key and a Divine Ember.
If you're interested in a final detour, now is a time to consider entering the sealed door near the bonfire. If you do enter it, you'll find that the area is populated by fearsome enemies. Many of them are human, but they're wearing cloaking gear that makes them difficult to see (and makes it impossible to lock onto them as a target). Not only that, but they have spectacular defenses and you'll have to hit them quite a few times to drain their life meters.
If you like, you can run from those enemies (along with other more familiar enemies in the area) and make your way toward the eastern slopes, which overlook a distant castle. There, you will find a corpse on the ground that you can loot for the Eastern Helm, Eastern Armor, Eastern Gauntlets and the Eastern Leggings. It's powerful armor.

The area is also a good place to farm for souls, if you're ready to get cheap. When you first enter, you're standing at the top of some stone steps. You can descend the steps and start forward into the trees to lure enemies toward you. Once an enemy or two is rushing you, head back toward the exit. As you're facing the steps that lead up to the exit archway, head around their right side on the lowest level. There's an extremely narrow ledge there, but you can follow it to its end and hug the wall. Any enemies that are chasing you will climb the steps and try to drop down on you from above, killing themselves in the process. You can get around 7000 souls per run in this manner, making it easy to build levels. It's cheap, but it works most of the time. Sometimes enemies will land on the ledge next to you and you'll have to knock them off, or the magic user will follow you around and pelt you with magic from a distance, but that's the exception rather than the rule.
Once your equipment is much better and your levels higher, it's worth coming back to the area to find a special boss, the Great Grey Wolf Sif. To find the wolf's lair, head forward from the entrance to the area. Proceed straight forward through some trees and past where you battled the four tough enemies. You'll come to a walled area. As you first enter, look to the left and there's a cat sitting in a window high on the wall. You can talk to her to join her covenant and receive the Cat Covenant Ring that lets you attack unwelcome players who enter the vicinity. Note that if you join the covenant, you're not to harm any creatures in the area, only unwelcome players who you can battle when you have the ring equipped. The exception is the wolf who lurks at the end of the forest.

There are some ruined stairs ascending ahead of you as you work through the area, but you can veer left and descend some stairs through the area to arrive at another chunk of forest. From there, you can either continue forward to find a rock ledge, or you can head to the right through the forest and find mushroom characters and a dangerous cat-like animal that will attack you even if you're in Alvina's covenant. You should avoid it if you want to remain on good terms with Alvina. If you decide to fight it instead, know that it is capable of taking a tremendous amount of damage, plus you aren't allowed to brush against it (even when it's not charging) because it has quills that will inflict damage on you. Try to take it out from a distance with fire magic, and make sure that you target it so you know where it is positioned and can dodge out of the way of its rolls.

If you go for the rock ledge, you can jump down from the rock ledge and head forward again to reach a mysterious gate. It's easily opened without any special equipment. Through the gate, you'll find a hauntingly quiet area. Ahead of you, near the edge of some water, there's a huge sword. When you approach the sword, a scene is triggered and then the boss wolf attacks.
Before you try to kill Sif, it's not a bad idea to join Alvina's covenant and to kill a few players who venture into the forest. Three or four ought to do the trick, but do yourself a favor and only attempt things when more players are likely to be online than just high-level players (the early AM hours can be brutal, with players that are leveled up to the point where they're essentially impossible to beat). Then you can talk to Alvina again and she'll ask you to hunt down the wolf on her behalf. It's an extra step, but one worth taking if you want a nice reward.
Grey Wolf Sif
Battling Sif can be tricky, as the creature has amazing range with the huge sword that it carries around in its mouth. Mostly, it will prance around the clearing and swing the sword back and forth, but occasionally it will pause and shake it briefly before resuming the swinging efforts.
You need to avoid being struck by the swinging sword at all costs. It can take away a lot of your life and even blocking a hit mostly drains your stamina. Your best bet is to roll out of the way at the right moment and get close to the wolf, at which point you can strike at its flanks.