Zero Hour--Clone Wars--Geonosis
After you hit the surface of the gladiatoral arena, you'll have to begin your journey towards Sun Fac on your own; don't worry, you'll be meeting up with your redoutable squadmates soon enough. For now, though, you'll have to maneuver through the trenches of the oddly corridor-ized arena--it sure looked a lot flatter in Episode II.
A few moments after you set down, you'll take a bit of damage from an "anti-infantry round" that seemingly came out of nowhere. This is unavoidable, but getting healed up is no great chore; just walk around the corner from the drop location and use the convenient bacta dispenser! You're going to find these things all over the place, luckily, even in the middle of Geonosian facilities populated entirely by robots, oddly enough. If you can find one in an area without a large enemy population, then you'll be able to heal yourself and your entire squad to full health. For now, just get yourself healed up and help the nearby troopers in their battle with the droids atop the walls.
Secure Area Around Crash
Your first objective is to bypass the droids and work your way along the path until you come to a crashed troop transport; the area is crawling with droids, and your task is to eliminate them until they die from it. There's an explosive barrel in the midst of the droids which you can use to blast a bunch of them; you can finish the rest off with your blaster or with your melee attack, which performs an instant kill when it hits a droid.
After the transport is safe, another path will open, leading to a little tunnel system. Fight your way through the droids--by now you'll have discovered that they only deal light damage to your shields, and aren't difficult to destroy, until you get your next objective.
Destroy Gun Emplacement With Grenades
Apparently there's a large artillery piece further down the trench; your only hope of destroying it is by picking up the thermal detonators from the ammo pallet and throwing one into the gun's open ventilation-shaft-looking-thing. You should get a red targeting reticule when you're aiming at the correct location, so chuck a grenade into the hole and watch the fun. The destruction of the gun will open up a new path; follow it to meet up with Delta 62.
Now that you have a squadmate along for the ride, you'll be able to destroy one of the walls blocking you from the Geonosian spire, which is your ultimate objective here. Command 62 to place a charge on the wall that the Advisor targets for you, then cover him while he does so--it'll take him ten seconds, so be sure no Geonosians hit him in the back. When that's done, you'll be able to detonate the charge and proceed through. A dropship will be required to blast through one last obstacle in your path--apparently the Clone Army was never given that critical "climbing over things" training--but it'll be called in automatically when needed.
Into the Hive
Rendezvous with Delta Four-Zero
Great, a bug hunt. The Geos aren't tremendously fearsome enemies, although they are mildly tougher than the battle droids you've been fighting so far. Anyway, in order to reach 40, you'll have to blast through another door; do so to meet up Fixer, another member of your squad. He's going to be able to slice doors and consoles for you, such as the one immediately next to his location. He's also likely to be injured when you meet up with him, so command him to heal himself at the bacta tank after you slice through the security door.
After you slice through the door leading to the hangar, you'll have to fight your way through battle droids and Geos until you spot a pair of Geonosian fighter craft; Advisor will ask you to blow them up with a charge, which you should do, since they're blocking the exit from the room. Most of the enemies here are going to be difficult to close in on due to the gaps in the floor, so don't forget to use your zoom feature to make your blaster fire that much more accurate when firing from a distance.
Next up is a darkened passage; you'll need to flip to your nightvision visor to see what's going on. The passage isn't very long, but the battle droids you're fighting against will be a bit more damaging than in the introductory level, so proceed slowly and use the crates scattered around as cover from their fire.
Eventually you'll reach another hangar, wherein there are yet more boxes to block your path. After tasking one of your commandoes with detonation duty, you'll need to stick close to him to prevent the Geonosians from bludgeoning him to death during the ten seconds he needs to place the charge before clearing out the rest of the room and moving on.