Get a Social Security number
Your key to tax benefits is a Social Security number. You'll need one to claim your child as a dependent on your tax return. Failing to report the number for each dependent can trigger a $50 fine and tie up your refund until things are straightened out.
You can request a Social Security card for your newborn at the hospital at the same time you apply for a birth certificate. If you don't, it can be a real hassle. You'll need to file a Form SS-5 with the Social Security Administration, and provide proof of the child's age, identity and U.S. citizenship.
If registering newborns strikes you as silly, keep in mind that the aim is to prevent taxpayers from claiming dependents they don't deserve (think parakeets and puppies). Apparently, it's working. In the first year the government required Social Security numbers, 7 million fewer dependents were claimed than the year before.