Kevin Ellway has written a very good article which is on the main website but i think you have to be a class member to view it. Alternatively there are some pretty good articles on how to build them with some theory on how they work in the Technical section of the website too.
I will defer to other more experienced sailors here but for a brief outline though: in order to reduce the drag caused by the transom you give the t-foil a bit of angle which will lift the back of the boat. You then move your weight backwards in order to bring the attitude of the hull back to normal sailing position (except you will be slightly higher out of the water due to the lift). This gives a speed advantage in that the drag effect of the t-foil is far less than that of the transom.
Obviously, the faster you go the more you can load up the t-foil, this can have some interesting effects if you don't move back enough. See one of the recent pics of Atum taking a big nosedive upwind. Downwind it can save you from fairly disastrous cartwheels, but you have to make sure you let it back to neutral when you bear away.
Personally I have not really mastered the t-foil and until I am able to sail the boat well, I am sticking to keeping it neutral all the time.