Earlier, I suggested that you only needed to learn four ice skating "techniques" before you could consider yourself 'fit' to jump into an ice hockey game ("stopping", "forwards skating", "backwards skating", and "turning (forward)"). These fundamental moves will at least allow you to participate in a game without too much trouble. To really properly enjoy the game, you will need to learn how to do pivots and backward cross-overs.
Backward cross-overs are turns made while going backwards. If by now you're about to skate backwards in a straight line, then learning how to turn while skating backwards is the next technique to tackle. Like going backwards in a straight line, drive your leg into a semi-circle, but instead of stopping underneath your bad, drive the leg past your center, to the other side. Your "planted" (or passive) leg will naturally skate backwards, allowing your driving/pushing leg to cross "over" the other leg.
Turn on any figure skating competition or ice hockey game, and you can observe people doing backwards cross-overs. I think this is a harder technique than pivoting, but since pivoting involves changing your direction, it helps to be able to do cross-overs in both directions first.