Doing Your Thing and Getting Out Again
Once you have located your quest object, you can do one of just three things: kill it, pick it up, or talk to it.
Killing it is just basic combat. To pick it up or talk to it, you must click on it. This will usually launch a message box. Do whatever you need to do, depending on the message, and leave.
Getting out can be easy or difficult. If you anchored a "Recall" somewhere, you're job is easiest. Just cast it again and you'll be teleported to wherever you set your anchor. Option 2 is to walk out. Just follow your map back to the entrance.
Option 3 is to (wait for it...) CHEAT! One of the features that Bethesda installed with the v.212 and v.213 patches was the <alt>+f11 hotkey. This was designed to pull you back out of the "void" when you fell into it. What the game basically does is to "remember" where you were for the last dozen or so times that your feet were on the floor. When you hit <alt>+f11, you are taken back one "step". But there was an unintended cheat that came with this. What happens when the game doesn't know where your last "step" was (as in when you reload a saved game)? The answer? It thinks that the entrance was your last position. So, if you save the game, reload it, and hit <alt>+f11, you'll be teleported back to the entrance. Just click on it and you're out.
Now you travel back to the NPC who gave you the quest to report and collect your reward.