What is the best way to level up?

Find a VERY strong monster that you are barely capable of beating, one that when u beat it, fill up ur exp bar around 30-50% after u kill it. Once u kill it, save ur game, then reload the game. If its a rare monster, u may need to load it a few times for it to respawn. Make sure the monsters level code isnt red or you wont be able to hit it

Definitely do quests. All of them! Or at least the majority.
I was slightly overleveled compared to the mobs almost all the time from doing most fo the quests, 2-3 levels above them, but it can make a huge difference :)

Yup, questing, achievements and farming rare monsters works for me :D

If the area you are currently in is too tough I suggest you return to previous areas and finish up any quests. Not only do you get XP but you can get good equipment as rewards too.

Don't forget to go back and fight some of the beasts that were too high a level for you during the earlier stages. You'll be suprised what gear they drop.

Hope this helps.

I'm now at the end of the game but i simply can't beat the final boss. The enemies in prison island are already too low for me, all the higher enemies i found elsewhere are too high (i am on lvl 80, they are 95+ so i can't even hit them) I wanted to do quests like the faq suggests but the npcs that are supposed to have them don't respond (and, yes i am talking to them with the right character). So i am pretty much stuck, unless someone can provide me with a good levelling area or i grind prison island enemies for 20 hours...

@Erimocard

Uh.. I beat the final boss at level 80. But if you must, I think I was beating Gogols when I was around level 80 at Satorl marsh near the statue landmark, or under spiral cave at Bionis Leg (in the cocoon things around Unique named spider)

I think the gogols in Satori Marsch are between 82-84. I think thats quite good. Beating a high level rare monster works too. You should need have a good combination.
When I was 55+ I went to kill flami in Bionis leg . They are level 72. The party setup that worked me was, melia, riki and Sharla. Sharla for heal, riki for poison chill etc. Sleep the monster , most of the things will stick to the monster. Melia is a great solo Job as well. try it out!

I'm beating the turtle on the eryth sea by going out of it's reach. Only gets me 8000 exp a time, takes 20 min..so not really worth it since quests can be 20000... but when it drops golden chests|!! Awesome gear for Riki a.o.!

Find a landmark (or a place that's near a landmark) that is filled with monsters that are at your level. Kill them all for some impressive XP, and just skip travel to the same spot. Repeat and rinse as much as you like. Same for any other areas you'll get stuck on ;)

Sometimes higher level enemies are the way to go. An easy method of felling such enemies quickly is to use either Melia, Riki, or both to inflict Poison, Chill, and Blaze and stack with the Plus gems to wittle them down to nothing. Sometimes having Reyn tank to soak up damage and aggro helps out greatly...especially with Melia. The EXP yield is well worth the effort.

You will want to mix doing quests with grinding on enemies.
For efficiency's sake, here is a game plan that works.
When grinding: Go up against white-difficulty enemies, one at a time. If you are having a difficult time against white enemies in your area, blues work too. Stay away from yellow-level enemies unless your gears are fantastic or your party is high enough in level for their stats to hold out against one.
Use the stone throwing ability[press down when highlighting your talent gauge until you see a purple arrow] to lure enemies that are grouped together to you one at a time, and never, EVER, face a large group all at once, for the sake of staying alive. One or two at a time may be fine, but not 4 or 5.
Reyn and Sharla are your best friends. Enough said. Third party member is up to you. I suggest either Dunban or Shulk, although Melia's buffs are nice once you've leveled them up a bit.
For quests: Accept each and every quest you can get in the area, then focus on the ones that ask for you to defeat certain numbers of enemies and special monsters[challenge side-quests] first and foremost.
Once those are done, go into your quest list, sort the list so that the New quests are what appear first, then focus on them one at a time starting at the top. That way you won't feel overwhelmed.

One last point: Don't be ashamed or against taking breaks.
Sometimes this game can get grindy to the point of frustrating. If it's getting to be too much, I suggest stopping for, like, 5 minutes to watch a youtube video or listen to some music to clear your head before diving back in.
Pacing is key.