Quesh is the shortest planet in the game, there are only maybe twenty quests for you to do on this planet and if you go quickly you'll be here for only about two hours tops. On your way through the Orbital Station you will come across a Republic Commando who has the first real quest for you with Quesh, "Venom Safeguards". After you have that quest in hand continue down to the surface of the planet and grab all of the quests you see here. Also turn in what you have before getting ready to leave town. You'll want to make sure you have the following quests before doing anything: "Venom Safeguards", "Extracting the Scientist" and your <Class Quest>.
Seal the First, Second, Third and Fourth Venom Pipelines
Easy quest, everything is marked on your map. The bonus quest tied to this one, "Heal the Workers" requires you to use the Quesh Venom Healing Adrenal from your inventory on the Poisoned Miners. They're easy to find, no further explanation is needed. When you go to refresh your Venom Safeguards quest you will notice a quest just to the north from Gallia called "Drilling for Imps". Be sure to pick this quest up.
The next three quests we have are all in the same area.
Extracting the Scientist
Sabotage 5 Security Stations
All of the Security Stations are easy to find since they're glowing blue. Although they're quite spread out you shouldn't have difficulty with this part. After you complete the 5 Security Stations objective your quest will update, telling you to Rendezvous with Agent Meldo. During these two parts you will want to do the bonus series tied to this quest. It's really easy to do and doesn't really require that much extra explanation.
After you rendezvous with Agent Meldo your quest will update again having you Investigate Doctor Orlian's Laboratory. As with all objectives before it, the laboratory is marked as clear as day on your map.
Drilling for Imps
Recover the Mining Drill Part
For this quest all you need to do is enter the Imperial Mine, kill your way through to the quest objective and grab the Mining Drill Parts.
Enter the Imperial Outpost
Once you make it inside the outpost you need to Sabotage the Anti-Aircraft East and South guns and then use the Comm Tower to signal an Airstrike. Also the bonus quest in here requires you to kill 20 Imperial Forces. Both guns are marked on your map.
If this is not south below the next town we're going to do it now. If it is wait until I mention it later.
After completing all of these quests you'll want to head south to the new town and turn in the quests you have there. Gather everything up that you find here and grab the Quick Travel Terminal as well as the Taxi Flight Path before flying back to the town up north. Back up north you have two quests to turn in, turn both of them in and then head west to Gallia and turn in your quest to her. After you've done that return to the town up north (I Quick Traveled but you can either run or fly back up here, it doesn't matter).
Once you're back up here it is time to start our questing again! Before leaving town you will want to make sure you have the following quests "Cartel Crushing" and "Venom Cleanup" as well as your Class Quest. The first quest we're going to be doing is "Cartel Crushing".
Destroy 5 Cartel Command Droids and Evacuate the Factory Workers
This is a fairly straight forward quest, there isn't any explanation that is needed, just follow the objective locations on your map. Once you finish the quest head back to town and turn in the quest and accept the new one. Depending on if you choose Light or Dark your quest will change here. I chose dark so I have "Storm the Sewers"
Destroy 5 Venom Tanks
Easy quest, the Venom Tanks are glowing blue and easy enough to find. Once you're done this quest it's time to get your Class Quest out of the way.
Get this bad boy out of the way now.
Storm the Sewers
Enter the Sewers
The Dark Side version of this quest has you sneak through the sewers and the light version has you going through the front gates. Both of which are easy, just follow the mission objectives and you'll be done before you know it.
After you complete all of your quests return to town and turn them all in. There will be a single new quest available to you which is the final quest of Quesh. From town you will need to head back down south and over to the location it shows "Reclaiming Quesh" on your Map.
Locate Broga the Hutt
The main quest for here is easy, there is no point in explaining that one. For the bonus series though, you'll want to eliminate the Imperials until you get to stage 3 at which point you'll need to destroy 8 Siege Equipment in the central open area of Grancha Lakand Venom Mine. There is a second bonus quest in here as well that requires you to access the Medical Terminal and then Heal the Poisoned Workers throughout the mine.
After you complete stage 3 you'll get the final stage of the bonus quest which requires you to kill the Siege Droid and loot his memory core. After that all that's left is to defeat the sith lord and Major Treeg. Doing so will complete this quest, at which point you should Quick Travel back to town and turn it in as well as the bonus you did.
You are now pretty much done Quesh, turn in whatever is left to turn in and then head back to your ship and use the Holoterminal to continue your class quest.