Vegan is pretty simple - no animal products. So no dairy, no eggs, no honey, no gelatin. (And, obviously, no lard or meat.)

The best vegan desserts I've ever had (besides these AMAZING cakes this woman here in the city makes - check to see if there is a vegan bakery in Houston) are fruit crisp type desserts. It's ridiculously easy to make fruit filling that is vegan - basically fruit, water and sugar. Then just make a crumb type topping, but instead of butter use a good vegan spread. My personal favorite is Willow Run soy margarine. (They should have that, or something similar, at Whole Foods or Central Market. Do NOT just use plain 'ol margarine, as lots of them contain either dairy by-products or gelatin.)

You can also check at places like Whole Foods for the vegan egg replacer, the name of which is escaping me. With that, some soy milk and soy creamer (which I've used successfully to substitute for half and half), and some soy margarine, you could make most of your favorite desserts in a vegan manner. And with some high quality cocoa powder, you could easily make a vegan chocolate dessert. (Might I suggest a chocolate bread pudding?)