There are two main kinds of tofu - silken and cotton.
Silken tofu is softer and smoother and more inclined to squoosh than crumble—it's had less liquid pressed out of it during the setting process. It comes in “firm” and “extra-firm” types, though neither is really all that firm. It's usually sold either in asceptic containers or in a bath of water. I think this is the more readily-available type in the US. I don't like most of the brands of the asceptic type I've tried. I think the one that I did like was Mori-Nu, but I could be misremembering. I like the stuff I get from the Chinese supermarket; it's in a water-filled box, chilled.
Cotton-style tofu is firmer and will crumble. This is the easiest type to find in the UK; most supermarkets sell it. “Cauldron” is a common brand. You can freeze this, and on thawing the texture will have changed, becoming much more spongelike, which is very useful for getting it to soak up seasonings. The longer you freeze it for, the more pronounced the effect.
You can also buy pre-fried tofu in most Chinese supermarkets, again in the fridge, in large cubes. This has more fat, obviously, but it also has more texture and it soaks up marinades really well.
Here are two simple methods for using cotton-style tofu. For both, start by rinsing some tofu and squeezing it gently with your hands to get a bit more water out. Then:
Pasta. Crumble the tofu and fry it in a bit of olive oil. Remove and set aside (optionally marinading in a mixture of soy sauce and red wine—sounds odd but tastes great), then fry onion, mushrooms, peppers, etc, put the tofu back in, add some canned tomatoes and herbs and stuff, simmer until done to liking, serve over pasta.
Stirfry. Cut the tofu into cubes, marinade in whatever stirfry sauce you're planning to use, stirfry veg as normal, add tofu with sauce and heat through. Serve over rice or noodles.
Silken tofu is often used in desserts.
Be aware that tofu has only a very subtle flavour of its own, so people unfamiliar with it may be disappointed and decide that it's “bland”. If you're hooked on strong flavours, be sure to add plenty of seasoning to your tofu dishes. I've recently seen the suggestion that tofu soaks up flavours better if you marinade it after frying, as opposed to before, and this certainly seems to be the case with the deep-fried stuff.
If you're not put off by the idea of eating something that doesn't taste very strongly, try a few types/brands of tofu plain and see what you think. I've had some very good-tasting tofu from the fridges in Chinese supermarkets; one was almost “cheesy”—too cheesy in fact for a friend of mine!
I was recently asked whether tofu should be treated as hamburger, or cheese, or both; and whether it would melt like cheese.
Tofu doesn't melt, no—if you want a vegan melty cheese type sauce, check out this post made to the alt.food.vegan newsgroup by MrFalafel.
Tofu can be used as a substitute for either meat or cheese. An example of the former: the pasta sauce described above. An example of the latter: blend tofu and seasonings (nutritional yeast and/or stock/broth powder, herbs, olive oil) in a blender and use instead of ricotta in lasagne or something.