If you're adjusting status (to a permanent U.S. resident, or green card holder) you'll need to complete USCIS form I-485 and select the appropriate forms and documents to accompany it.
By using Form I-601, certain foreign citizens who are ineligible to immigrate to the United States because they are "inadmissible" can request a waiver (forgiveness) of inadmissibility.
In order to apply for a B-1 (tourist) or B-2 (business) visitor visa, you will need to complete a few forms and submit supporting documents and various fees.