To qualify as a carryon, a bag must be small enough to fit in the overhead compartment. Bags that do not fit will be checked once you board the plane. You are allowed one carryon and one personal item per flight. The rest of your luggage must be checked. Many airlines will charge you a fee for checked bags; the price varies based on weight and airline.
As of 2010 you may carry three 4 oz. containers of liquid with you on the plane, as long as they are in a zipped clear plastic bag. Baby food, formula, breast milk and medications may be taken on board in any necessary amount if they are declared at a checkpoint ahead of time.
You may not take any sharp objects on the plane with you. Firearms are also prohibited. You are allowed a personal lighter, but no other device that makes a flame.