Before entering the U.S., most visitors are required to apply for a visa. You can determine which visa you might qualify for from this article on types of temporary visas.
Applying for a tourist visa is most commonly done at the embassy or consulate nearest you. The U.S. Department of State's website lists embassies and consulates near you as well as providing other useful, up-to-date information before traveling to the U.S. Once you've located the nearest embassy or consulate, check their website or call them for information about whether they want applications to be done in person or by mail.
Applying for a tourist visa depends largely on what type of visa you are trying to obtain:
One of the final steps in applying for a tourist visa is going in for the visa interview. The visa interview isn't like an employment interview, but it's also not just a formality. Prepare for some of the most commonly asked questions, show up early, be polite and make sure you request an interpreter if you do not speak English. In general, the interviewer is trying to verify that your application is accurate, and establish your "ties" to your home country (ensuring that you will return after visiting the U.S.). Here are some of the most common questions you may be asked:
Check with both the Department of State and your local embassy or consulate to get a feel for how long it will take. Tourist visas will typically only take a few days (but can take longer), student visas will take slightly longer and work visas can take months. This is in part due to heightened screening requirements, background and criminal checks, as well as increased reliance on mailing applications and requiring interviews. So do not leave this until the last moment, otherwise you may not be able to travel at all.
Contact a qualified immigration attorney to help you with visa procedures.