Amateur Adult Hockey League. C Division which is for people like me with little or no organized hockey experience. I'm 26 years old.
Ok, so it's probably a little more laid back and not so precise at that level. When you start out just ask how they're changing. If it's position for position just ask "Who am I changing for?" and they'll tell you the one person you're supposed to go on for. Just keep an eye on that guy and when he's skating towards you begin to hop over the boards.
If they're doing a rotation of next forward just keep track of what number you are in line. The first in line is usually the one who's been on the bench longest at that point. The person that just hopped off the ice will be last in line. When you're #1 in line and someone's coming off, get your butt over the boards, haha.
For a good change, ideally you'll be flying off the boards and beginning to skate away as he's reaching the door/hopping the boards. You don't have to wait for him to take a step off the ice, you can both be on the ice for a second or so, but only as long as he's showing effort to get off. Just make sure he's intending to come off before you go flying out.
Also, as Fanned On It said, if you hop on the ice and the guy you're changing for isn't completely off yet don't touch the puck. That'll get you called for Too Many Men most likely.
Just try not to change like this:
Edit: Here's a great video of the Sabre's bench. Watch how a player on the bench will hop over and skate away a second or two before their guy even gets to the bench. If the puck's deep in either end it's not that important to be super fast on the change but if the puck is around the bench area you don't want the players coming off to be lollygagging like they are in this video.