Group your zealots into one group, and dragoons into another. Now proceed down the ramp, then north to the bridge. You'll fight two battles on the way, the first is just a couple of zerglings. The second is several zerglings and two hydralisks. Make your zealots take all the damage while you focus fire with your dragoons. You probably won't lose any units even during this fight.

Cross the bridge then fight the zerg there. You might lose a zealot here, but so what? Now head on south toward the Protoss base where you'll kill some zerglings. There you'll meet Fenix, and gain control of the base. Build about eight probes (pausing to build a pylon when you must, be sure to place it by the gateway) and set them to gathering minerals, then get three more on vespene duty. Warp in a cybernetics core so you can build dragoons, and get their ranged attack upgrade. You should also research ground weapons at your forge. Now place a photon cannon at the entrance of your base as Fenix suggested.

You can now build some more pylons to support a larger military. I recommend eleven zealots with Fenix and six dragoons be taken with you on your attack on the Zerg base. You should leave a couple zealots and dragoons home to defend your base, also. You should begin your attack on the enemy base at this location (see screen) dead north of your base. Focus your dragoons on the mutalisks which will inevitably attack you. Keep your eye on Fenix, because if he dies you automatically lose the mission. He should be able to hold his own with such a large escort of zealots, however. The main base is to the west of this ramp, it's not very big but is pretty well defended for a first mission. One thing you want to make sure to take care quickly, once you reach the base proper, are the sunken colonies. Don't let them deal lots of damage to your units. Focus your zealots on them as quickly as possible while your dragoons cover for them.