On June 1st you will need a passport or a passport card to enter the United States. Get a passport; the cards are very limited in use. The cards are only good for land and water entries from Canada, Mexico and the Caribbean. If you are on a plane or coming from another destination you will need a passport.
Passports cost $100, are good for 10 years and are pretty simple to get. Here’s all the information you need: http://travel.state.gov/passport