Here is one that I posted in FO. It's very basic but a good start.
You can't use your stick to trip somebody, hit them in the face, spear them, hit the stick out of their hand, slow the other guy down, etc.
You can't barrel through somebody going full speed; you can't slam into them when they are up against the wall; you can't elbow them; you can't hit them a specific distance from the boards because that can seriously injure them; you can't block anybody like they do in football; you can't intentionally hit the goalie.
Any of the above rules are either a 2 minute, 4 minute, or 5 minute penalty depending on the severity of the penalty. That initiates a power play. 2 minute power plays are 4 on 5 and the team with 4 gets their 5th person back after either A) 2 minutes pass, or B) the team with 5 scores. 4 minute penalties are the same way but the team with 5 gets 2 chances to score. A 5 minute penalty is a major penalty and the team with 5 can score as many goals as they want without the 5th person coming back on.
All players must be behind the blue line when the puck crosses the blue line (offsides), if the puck is hit down the ice from behind the red line and nobody touches it then it is icing (the team that committed icing cannot substitute players and the puck starts in their zone), the defense can't shoot the puck over the glass in their own zone (this triggers a minor penalty for delay of game).
I'm leaving a few rules out but those are the major rules and most common occurrences. You can play 4-on-4 with penalties (both teams receive penalties), 3-on-4, and 3-on-3. You can't do fewer than 3 though.