How can a non-immigrant become a US citizen?

A foreign national cannot go directly from being a nonimmigrant to a citizen, but instead first must become a Lawful Permanent Resident (get a "Green Card"). Then, after being a Permanent Resident for 5 years (3 years for most Permanent Residents married to U.S. citizens), the foreign national may apply to become a naturalized U.S. citizen. Eligibilities to become a Permanent Resident generally are divided into those involving family relationships (e.g. being the parent, child, spouse of a U.S. citizen or Permanent Resident) and those involving employment. Of course, there are many, many, other details that can determine eligibility for Permanent Resident status and, later, determine eligibility for naturalization.