Get a passport. You'll need a passport to travel to almost any foreign country these days. Whether you are going to Europe, Asia, Australia, or some place else, you will probably need a passport.
Register with an embassy. You will need to register with the US Embassy in whatever country you are living in. This allows people to get in touch with you if there is an emergency back home.
Find out how long you can live in the country you are staying in. Once you discover that, decide whether or not you want to come back home, or start the proceedings to make you a naturalized citizen of the country you are living in.
