You are allowed to bring one carry-on and one personal item, such as a purse, onto the plane with you. The TSA prohibits guns, ammunition, sharp objects, tools, explosives, flammable items, chemicals or candles. These will be, at the very least, confiscated.
One quart-sized, clear, zip-top bag is allowed per passenger containing 3 three oz. bottles of liquid. This is commonly known as the 3-1-1 rule. Medications, baby formula and food, and breast milk are allowed to exceed this rule but must be declared at checkpoints.
Generally two checked bags are allowed per passenger, however this is dependent on individual airline rules. Explosive items, gun powder, chemicals and flammable items are not permitted in your checked baggage. You may check most other items that are prohibited in your carry-on luggage, including firearms and sharp objects as long as they are wrapped in protective coverings.
Firearms must be unloaded, packed in a hard-sided case and declared to the airline when you check in. The container housing your firearm must be locked. You must check with your individual airline to see if they allow ammunition to be checked. If they do, it must be packed securely in packaging specifically for small amounts of ammunition.