There are two main paths to becoming an NFL coach (meaning assistant coach, for most of them).
The first is to be a player, perhaps of marginal talent, perhaps on the higher end of the talent scale, who stays in the game through mastering technique and strategy, studying film, and hustling. When your career ends, you impress a coach enough for them to bring you on as an offensive or defensive quality assistant, and work your way up. (e.g. 49ers linebacker coach DeMeco Ryan, or perhaps, later, Richard Sherman.)
The easier path is to have a dad (or maybe a brother) who’s a coach.