Here are two examples to give you an idea of when to use each one:
1) Q: How many beers do you want? A: One (Eins)
2) Q: How many beers do you want? A: None (Keins)
Keins is basically the negative form of eins. So, you could say "Ich moechte ein Bier bitte," (I'd like a beer please) or "Ich moechte kein Bier danke." (Thanks, but I don't want a beer.)