Basicallly, the great artist got split up into four different Great People: Artists, Musicians, Writers, and Artifacts. The first 3 are all great people that you train from their own special guild (Artists', Writers', and Musicians' Guilds) or buy with faith when under the appropriate policies. You can either do a 1 time "culture bomb" (each are slightly different, Musicians do a Concert Tour that gives a big boost to Tourism influence with whichever Civ you send them to, Artists start Golden Ages, and Writers give you a lump sum of Culture), or choose to make a great work. You must have "slots" of the appropriate type to make a Great Work - so, for instance, if you have the Great Library, you have two slots for Great Works of Writing.
At this point, check with what Dirty said. Find each wonder or improvement in your culture screen, and mouse over the box, and it'll tell you what you need to do for your theming bonus. Its different for every Bonder or building, and not every Wonder or building has a theming bonus. Theming bonuses are basically like a quest with the objective of collecting a certain amount of specific Great Works in the slots. So if you just have any old Great Works, you'll get your normal Tourism score for those individual Works..but if you have matched all your slots correctly, you get a bonus in Tourism from the Wonder/building itself.
As far as I know, the only way to move a Great Work is to trade with the AI using the culture screen, or to just move the Great Person near to the city you want to slot him in and hope for the best. I've heard mention that you can actually swap within your Civ somehow, but if that's the case I haven't found it yet.
