Generally, if you want to visit (and not live) the United States you must first obtain a visitor visa. Travelers from certain countries may be exempt from this requirement. The U.S. Department of State administers the program.
Naturalization is the manner in which a person not born in the United States voluntarily becomes a U.S. citizen.
If you were born outside of the United States, there are two general ways to obtain U.S. citizenship through U.S. citizen parents. You can acquire U.S. citizenship at birth (acquisition) or you can derive citizenship from your parents after your birth but before the age of 18 (derivation).
A Permanent Resident Card (USCIS Form I-551) is proof of your permanent resident status in the United States. It also serves as a valid identification document and proof that you are eligible to live and work in the United States.