First, raise a lot of money. Without a pile of cash on hand, you won't be able to pay faculty and staff, or buy land, buildings, and textbooks. Many universities—Vanderbilt, Stanford, Carnegie Mellon—were started by moguls rich enough to pay the bills themselves. Others relied on foundations to jump start their endowment.
In most cases, the endowment is overseen by a board of trustees. The majority of colleges are not-for-profit institutions, with all the usual exemptions from income and property taxes. Donors can also write off contributions. In exchange, schools have to reinvest earnings and follow prohibitions against political activism.