don't eat meat! going veg is the best thing you can do for the animals. it is also the best thing you can do for your health & it's much better for the environment. need some convincing? check out these reasons. if you are really inspired, going vegan is even better. a vegan= someone who doesn't eat meat, dairy, eggs, or other animal-derived products; doesn't wear leather, fur, wool, etc.; doesn't use products tested by animals or those which contain animal ingredients.
don't wear something from an animal. the most obvious one is fur. never ever wear it and if you see someone wearing fur (make sure it's not a fake) tell them your opinion. don't wear leather or wool either.
write letters. they may seem small, but they often have much effect. making phone calls and writing e-mails are other options. Check out my letter of the week. also,
here are peta's action alerts that have many (often updated) phone numbers, addresses (e-mail & regular).
if writing isn't for you, do something else. volunteer at a local animal rights group or even start your own.
tell others about animal rights issues & get the word out. make a web site, put animal rights bumper stickers on your car, leave leaflets and magazines (many animal rights groups will send you some in the mail for nothing or next to nothing) where others can read them (in the bus, waiting rooms...), or anything else you can think of.
read. educate yourself about animal rights. there's many great books out there on animal rights and lots of sites with good info. see my things to see page. "animal liberation," by Peter Singer, is the major book of the animal rights movement.
that should get you started. remember that every thing you do, even if it seems small, really helps. Good luck!!!