At two, your child can easily hold a small cup, especially one with two handles (as many children's cups have). But these days most parents give their children sippy cups, which don't spill when tipped over.
Sippy cups are practical because they are neat and don't require you to help your child drink. Still, they can make it very easy for a child to drink too much juice or milk. If possible, offer your child a sippy cup when you're in the car or when you don't want a spill. The rest of the time, offer her a regular child's cup.
There are other types of cups in addition to sippy cups that can help your child learn how to be responsible. For instance, there are two-handled cups that are easier for small children to carry. You can also find cups with flip-up lids that, though they'll spill if turned over, enable a two-year-old to drink from them more easily than do other cups. You can also get cups with attached straws, which children love.
What is important about cups is not the type of vessel but how much liquid it contains: Don't fill any cup too high. An inch of liquid in a cup for a two-year-old is fine at any given time. That way the cup is less likely to spill, and even if it does, not too much liquid will fall on the floor or on your child. Also, if you only serve an inch of liquid at a time, your two-year-old will be less likely to get too much in her mouth at any time.