Hiya, I used to be vegan for a while and one of my best friends is as well.
Basically cut out any dairy products (so milk and eggs, like you said). I use rice milk or soy milk instead, which are both lower in protein than regular milk. Any by-products of milk are also out: cheese, butter, cream. Margarine usually tastes just as good (and again, lower in protein). Check any lollies you're eating in case they contain gelatine, which is made out of animal waste products (hooves, horns, etc). Check most ingredients for animal by-products like gelatine. Here is a list of E numbers that are not suitable for vegans http://www.veggieglobal.com/nutrition/non-vegetarian-food-additives.htm
Some vegans also choose to eliminate honey but I think it is for reasons of ownership rather than animal cruelty.
The other thing you need to watch is a lot of vegan recipes contain really high levels of protein through nuts, beans, lentils and tofu. Always ask about what ingredients are used or whether what you're eating is derived from nuts/beans/tofu.
And, if you're going vegan for animal cruelty reasons, remember it extends past your diet into products like leather. Buying synthetic leather vegan shoes and handbags will also help your cause