Kinds of jokes to tell a girl to break the ice include short one-liner jokes and short stories. Most jokes to break the ice are light-hearted puns or a play on words intended to make the listener laugh.
An example of a joke that breaks the ice is asking the person what kind of bone a dog can't eat. The answer is a trombone. A pun-style joke example is telling the person that the way to make an egg laugh is to tell it a yolk.
A longer joke to break the ice includes a joke in which a doctor says that she is about to pull the plug on an old woman. The old woman's daughter responds in surprise, saying that she thinks the old woman is healthy. The doctor agrees that the woman's health is good, but says that the woman is taking a bath and it is about to overflow.