Those that were not born in the United States and have not acquired U.S. Citizenship from their parents, will need a Visa or Green Card to enter the country.
Generally, a tourist Visa can be requested at a U.S. Consulate abroad by filling out an application and presenting documents of having strong ties to his or her country of residence.
Work Visas are granted to workers that are sponsored by an American company, and are subject to very strict rules. Because it is very complicated to obtain a work Visa in the U.S., many immigrants come with a tourist Visa and just stay in the country illegally. Many immigrants that are unable to even obtain a tourist Visa decide to enter the country illegally, by walking through the Mexican or Canadian borders.
Immigrant with illegal status have very limited options to regularize their position with the U.S. Citizenship and Immigration Services. Generally, those that overstayed their Visa can only get a Green Card if they marry a U.S. Citizen. Further, those that entered the country without a Visa have to go through a complicated waiver process, which require the assistance of the best immigration lawyers.
Other ways to change to a legal status are provided by special laws, such as the U Visa or the VAWA provisions. Finally, many illegal immigrant get legal status when the U.S. Government passes immigration reforms and amnesty laws.
Another common ground of ineligibility for immigration benefits are criminal convictions. Unfortunately, many immigrants do not understand the immigration consequences of criminal convictions when they plead guilty to even minor offenses, such as shoplifting or possession or controlled substances.
If your Visa or Green Card is denied, you will be given a written explanation of the denial reasons. You will be able to appeal a negative decision to a higher authority, which will be the Administrative Appeals Office or the Board of Immigration Appeals.