Czerka Landing Port
Objectives: Find the Star Map
When you land on Kashyyyk for the first time, form up a party with Zaalbar in it and leave the ship; you'll be hit up for a "landing fee" by an employee of the Czerka Corporation. It's only 100 credits, so you might as well pay it, but you can attempt to Force persuade the Ithorian into dropping the fee if you're capable of doing so.
Once you're done with that little run-in, take someone with a high security score and bust open the footlocker on the dock; there's an interface visor inside that's worth having, since it adds four to demolitions, computer use, and security. Even if you have poor scores in those skills, the bonuses may help you out in a jam; if you run into a lock you can't pick, you can attempt to equip the interface visor rather than switching out party members to see if that will help. At the very least it'll save your computer use expert one spike for every hacking action.
Proceed down the ramp to learn more of Zaalbar's backstory, and talk to Eli Gand to pick up on the Honest Debt side quest. When you reach Janos' office, speak to him for a bit of information about the slaving operations that Czerka runs on Kashyyyk, and be sure to look at the caged Wookiee off to one side to stoke your righteous indignation a bit. Oh yeah; they'll pay for this. They will definitely pay.
For now, let cooler heads prevail; you can even shop for weaponry with Janos, though most of it is non-upgradeable. Proceed to the Great Walkway.
The Great Walkway
Objectives: Find the Star Map
Forest Kinraths immediately attack you; tag em and bag em. There are Czerka guards ahead that have killed a Wookiee; you can either goad them into attacking you by protesting their actions for Light side points, or just go ahead and slaughter them if you're of the violent sort. Zaalbar has some pretty amusing comments here if you ask him whether or not the sight of the dead Wookiee makes him mad, though egging him on will cause a Dark side shift. Search their bodies for a Czerka key card. You can use this at the supply station elsewhere on the Great Walkway to open a couple of locked supply containers, if you don't have adequate Security points.
Continue along the path and head to the north when you hit a fork in the road. You should have your first encounter with one of the Dark Jedi groups that Malak has sent to hunt you down. Don't worry; these guys aren't anywhere near as difficult as the fight with Juhani may have led you to anticipate. You can take them down with relative ease; be sure to search their bodies for lightsabers and crystals. If you're dual-wielding lightsabers, or even if you're not, you might want to make a trip back to the Ebon Hawk to upgrade your sabers with the new crystals; the short lightsabers you found will let you dual-wield without quite as much of an attack penalty. You'll eventually run into a Wookiee guarding the entrance to the village of Rwookrrorro. Un-equip Zaalbar before you get too close to the guard; he'll be leaving your party, and any equipment he has on him will be inaccessible to you for a while.