Signups are usually in January or February. Ask parents with older kidz where they play baseball, why they think it's a good league, and how to sign up.
Some cities post signs in prominent places.
Others will send literature home from your child's school. Usually, you get a discount for each additional child. If your child is a skilled player, some leagues will let your child play on a team with older kidz. I would discourage it. Most likely a copy of your child's birth certificate.