The rule is 3-1-1 for carry-ons. Each passenger is allowed to bring one zip-locked quart bag with liquid contained in 3 ounce or less bottles.
All adult passengers are required to show a U.S. federal or state-issued photo I.D. that contains the following: name, date of birth, gender, expiration date and a tamper-resistant feature in order to be allowed to go through the checkpoint and onto their flight. If the passenger cannot show this identification, then they will be screened in depth by a Transportation Security Agent.
Many items, such as explosives, are never permitted on an aircraft. However, some items, such as baseball bats, can be checked, but cannot be carried on to the airplane. For a comprehensive list of prohibited items, see the TSA website listed below.
If you are bringing a gift as a carry-on item, do not wrap it. Often, a TSA agent will be required to unwrap your gift to verify the contents.