Visit the U.S. Department of State travel website (see link in References). It not only will give you all the latest information on travel warnings and alerts, but it will tell you if you need a visa for the country you are visiting and how you obtain one.
Go to a nearby embassy of the country you are visiting, or visit the website for traveling to the particular country to see if you can apply for the visa online. LonelyPlanet.com will often have information regarding how to apply for particular visas for different countries (see link in References).
Pay the set fee, which will vary from country to country. Depending on what country you are traveling to and how you applied, you may have to wait several days to a few weeks before your travel visa is given to you.
Travel to your desired country. Your visa will not begin its set time period until you enter the country. If a visa is given on your arrival, you will receive it while going through customs.