If you only want to have a marriage in the United States, but not live in the U.S., you can apply for a visitor visa or tourist visa, known as a B-2 Visa. The application process is probably the easiest and fastest in the immigration law field; however, it carries certain risks.
First, there is the risk that the consulate believes you are getting the visa under false pretenses. You can tell the consular officer that you intend to use the visa in order to get married to a U.S. citizen or plan a wedding. Otherwise, USCIS may later claim that you obtained the visa through fraud (pretending to be “only” a tourist), which can prevent you from getting a green card if you want one later.
Second, you could face problems at the U.S. border when you enter. Even after you’ve convinced the consular officer that your intention after marrying is to return to your home country, you’ll still have to convince the U.S. border official. If you get a reasonable official, this should be no problem — your use of a tourist visa is perfectly legal. If you get an official who is inclined to be suspicious, however, it’s another matter and your marriage in the USA may not happen.
The border officials can keep you out if they think you’ve used fraud to obtain the visa, such as having lied about your intentions to return home after the wedding. Once you’ve been removed this way, you may be prevented from reentering the United States for five years. This is called expedited removal process. The border officials have reason to be suspicious, since many people have used tourist visas as a way to enter the United States precisely for the purpose of applying for a green card.