How does a college become a university?

As there is still no official, universal set of criteria to be a university, many states have their own criteria. For example, in West Virginia, the criteria to be a university states that the institution must offer at least one Master's degree, obtain approval from the Higher Learning Commission of the North Central Association, and have a faculty where at least two-thirds of the faculty hold the terminal degree, usually a doctorate (Mullen). In New Jersey, the process is a little more rigorous:

To qualify for university status, an institution must meet national standards for inclusion as a master's college or university in the Carnegie Classification of Institutions of Higher Education and demonstrate that it has met New Jersey eligibility criteria for at least five years. These New Jersey criteria require the institution to demonstrate that it has: a broad range of baccalaureate degree programs as well as graduate studies leading to masters' degrees in at least three areas; graduate students who demonstrated superior achievement at the undergraduate level; faculty whose competence is known beyond the institution; and resources to support graduate education, including laboratory facilities, library support, and financial support for graduate student and faculty research. While some states have acted legislatively to confer the university designation to all qualified public institutions en masse, New Jersey has opted instead for a rigorous review process that enables public and independent colleges that meet these criteria to seek university status. Not every institution that offers graduate programs will choose to do so. The process begins with a petition of intent and a detailed proposal filed with the New Jersey Commission on Higher Education, the state coordinating body for higher education. Then, two recognized authorities on graduate education who are independent of all New Jersey higher education institutions must complete a comprehensive review and report favorably on the proposal. Finally, the Commission considers the matter, voting to confer university status and approving a name change if it finds that the institution meets all requirements. - Hammond-Paludan

Massachusetts, will only grant a school university status if it grants at least two doctoral degrees. In general, to be a university, the institution must offer undergraduate and graduate degrees with many subjects or schools within the campus system, and can include online and remote programs.

Mullen, J. Michael, (2004). Chancellor's Interpretive Memo No. 15. Criteria for Designation of University Status. Charleston, WV. Retrieved May 28, 2012 from https://www.wvhepc.org/resources/intpmemo15.pdf.

Hammond-Paludan, Martine (1998). Editorial on University Status. New Jersey Commission on Higher Education. Retrieved May 29, 2012 from http://www.nj.gov/highereducation/news_releases/oped4.htm.

Massachusetts Board of Education: Degree-granting regulations for independent institutions of higher education" (PDF). Retrieved May 29, 2012 from http://www.mass.edu/forinstitutions/academic/documents/610CMR.pdf.