The first rule: An FBS team can have 85 scholarship players at a time.
Unlike most other college sports, football at the top level is a head-count sport. That means those 85 scholarships are full rides for 85 individuals. There’s no dividing the value of scholarships among teammates.
The second rule: An FBS team can bring in 25 new scholarship players in one signing class.
The limit is on 25 “initial counters,” which you can think of as players in their first year on an athletic scholarship. But a team can bring in more than 25 enrollees in a given year, in a few circumstances. Most commonly, if an athlete graduates high school early and enrolls for the spring semester, and if the school stayed under a cap of 25 in the previous year, it can assign enrollees to the previous class, up to the 25-man total cap.
If a player wants to delay his enrollment until the following spring, he can then be assigned to the following year’s class. But all players must be attributed to either a prior, current, or future class, and no class can exceed 25.
The only exceptions are Army, Navy, and Air Force. Every service academy student is on a non-athletic scholarship anyway, though those teams have a long list of other recruiting challenges that more than levels the playing field.
Conferences have their own rules, too. The SEC has a limit of 28 signees between December and May, which limits how many players a team can enroll early to avoid breaching the 25-man cap. The Big Ten’s rule is similar and also features a cap of 28 per year.