Go you!

You can do it!

In the book Vegan Freak (you should read it-it's great!) Bob and Jenna say you should just cut out all animal products immediately-right now. I suppose that could be hard for some people, though...
I'd suggest writing up a list of things you eat/drink that aren't vegan, and finding substitutes for them. It's pretty easy if you don't eat lots of processed foods, just have soy milk, rice milk, etc. and soy icecream, soy chocolate, etc. instead of dairy, and your prett much there I think...
My advice: Do lots of research! You might find that things you thought were vegan are actually not. Also, you can get LOTS of recipes, ideas and advice off places such as the internet.
Also, make sure you get your Vitamin B12! You can get it in tablets (make sure they're vegan) or supplemented in food and drink, such as soymilk and fake meat (check the labels to make sure). It's probably best to have both tablets and fortified foods, to be on the safe side.
This might help:
http://www.unleashed.org.au/change_the_world/go_veg/what_to_eat.php
Good Luck