How can a 13 year old girl earn extra money?

Well, as many people have mentioned, babysitting is one of the greatest way for someone your age to earn money. Although, if you wait until you're fourteen, and if your parents agree, you may get a job. If you wouldn't like to wait, try offering to cut other people's grass, and in the fall rake their leaves, in the winter shovel snow, etc. You just need to make yourself known. You could even put up posters saying, "Thirteen year old girl doing housework for paying customers." That way, the labour isn't too hard, and you still get money for it.