You're like me when trying to manage a team in FIFA, having been so used to hockey and baseball.
The salary cap basically works like this: there is a minimum total salary amount and a maximum total salary amount (the specific amounts are specified at the beginning of the season, this year the bottom is roughly 53mil, top is 71.5). All teams must have a total team salary that is somewhere in that window. That's why you'll see some teams with 60 million in salaries, while others right at 71.
Waivers apply when sending a player back and forth between your NHL and AHL (minor league) team. If a player does not have to clear waivers, you can move them up and down as much as you'd like. If a player does have to clear waivers, it means the rest of the teams in the league have the opportunity to basically take the player and their contract from you. It's worth paying attention to as sometimes you may be hoping someone will take a contract off your books, while others you may want to think twice about who you're calling up and sending down (i.e. in my BaGM last night I had to call up a player due to multiple injuries, but opted for a lower rated guy because I didn't want to lose my higher rated option when I inevitably sent him back down).
The draft happens once per year, in June, and is where you have a chance to select the future of your team. It will all be 18 year old kids from the junior leagues in the game, and the work you do in the "scouting" section throughout the season comes in handy here as far as trying to figure out who's the best pick for you to make each round. Many times these players aren't ready to make the jump to the NHL the very next season, but you can try them out in preseason and make a decision from there.