If you have a non-immigrant visa, then there is no real path to becoming a U.S. citizen. You can marry a U.S. citizen while traveling in the United States, however, which changes your immigration status and allows you to begin seeking permanent residency. You cannot travel to the United States with plans to marry a U.S. citizen, however.
If you have an immigrant visa, then you have a clearer path to citizenship. As an immigrant visa holder, you are considered a permanent resident of the United States (i.e. a green card holder).
After living in the United States for 5 years as a lawful permanent resident, you can apply for U.S. citizenship. The path to citizenship is long but maybe worth it for some individuals.