You can go for a visit, but not to stay, if that was your plan. Besides passport and visa, you need a round trip ticket and money for a place to stay while you are there. People that can't show that they have enough money can be turned away.
1) Get a passport.
2) Get a visa, if required (depends on your passport, length of stay, purpose of visit, etc.)
3) Book flights and/or other travel.
4) Off you go!
Since you're a first-time applicant, here are the detailed instructions, fees, etc. http://travel.state.gov/content/passport...
You get yourself a passport. Then you verify with the embassy of the country you wish to visit if you will need a visa (no visa needed for Europe, but one needed, for example, for Russia). You look at such as expedia.com for plane tickets and such as hostelworld.com for lodging.....and figure that you will need about 150$ per day (food, local travel, entertainment etc).
many us post offices are able to accepy passport applications
you need passport
