I run at a mid-major D1 school. A few athletes from every team are randomly selected four times per semester/eight times per year. As far as I know one or two of those are NCAA mandated tests where the NCAA sends a tester to the school to conduct the test. The others are facilitated by the school and results are reported to the NCAA.
The school has the right to non-randomly select individuals for tests if there is a reasonable cause (i.e. getting caught/arrested at a party with drugs present). The school can also non-randomly test part or all of a team immediately before/after a practice or competition if the coach feels it is necessary.
The random selection does not account for who was picked last time; I have some teammates who are freshmen and have been tested twice already and senior teammates who have been tested once in four years.