Every time you take the quest you are given a random quest from a list of (idk) about 6 different quests. You really only know what to do by running your mouse over the new action bar that shows up and reading the button descriptions. Some are easy and some are near impossible, however, you cannot change the quest you are assigned by dropping and re-taking, the same quest will appear until you complete that one.
This is all part of the "waiting game" quest line. The interesting thing is that you yourself do not have to do these Phiksi Yates quests as long as someone is doing them, so if you are stuck on a particular quest, you could perhaps convince someone else to take a quest and you can help them. As long as about 6 of these quests are completed you can look for the zone message that 'the barrier has weakened' and continue on with the quest line.
Oh, and note that this is a group quest, and they are not kidding. If you go in by yourself you will most likely not complete the quest.....and you only get the one shot (unless you are lucky enough to get in on someone elses quest). Having done this three times on different characters, my recommendation is to put this one off till you are at least level 60 and have some gear. Oh, and if you die in the final battle do not res out, there is a chance the NPC's will complete and you still get credit lying on the floor, whereas, if you res out, you are not getting back in.