Question about draft/prospects

So one area I still feel woefully uninformed about is how the draft and prospects process works.

I understand vaguely that some guys remain at their schools, European teams, or other misc I am probably missing but how is that decided? Is it based on commitment/contract? And how is it determined when they come over to the team? Is it when or if they sign a contract once the FO determines they’re ready? And is it always the Amerks, then the Sabres? How long to draft picks get before they’re waived(?) or not picked up or whatever?

For context I have only been a hockey fan for about 12 years in a state that has next to 0 other fans, and no family legacy of hockey fandom to speak of. I am an upstate transplant so I have been Sabres the whole ride, but it’s one of my big blind spots.

I don’t know, I feel like a moron and I am worried I am going to get eaten alive but I really honestly can’t figure it out and just don’t understand the timelines and process.

Please don’t hurt me…