I noticed that Saquon Barkley has an extremely high salary. How is a rookies salary established after the draft if the player does not have a choice on which team he goes to?
The 2011 Collective Bargaining Agreement (CBA) defines how much a rookie contract is worth, based on the position at which the player was drafted; for 2018, the top end numbers were that the first draft pick (which turned out to be Baker Mayfield) would always get a four-year contract for $33.0 million with a $22.2 million guarantee; the second pick (Barkley) would always get a four-year contract for $31.5 million with a $21.0 million guarantee.
While you say this is "an extremely high salary", it's worth noting that the 2006 CBA did not set rookie salaries, and this change deliberately reduced rookie salaries; the first pick in 2010, Sam Bradford, signed for $86 million with $50 million in guarantees, far more than Mayfield's contract. As the salary cap was unchanged, this had the effect of increasing veterans' salaries. The ethics of the existing players voting to reduce future players' income and increase their own is an interesting one.