The rule you may come across that you don't know how it works is the offside rule, thankfully it's not as difficult as the one in football so it should be easier to explain. For the explanations i will assume that you are the team shooting 'up' the ice.
Offside
In the middle of the ice there are 3 lines, one red one and a blue line either side of the red one. The blue line furthest from your goal is the one you want to worry about. You need the person who in in control of the puck to be the first person on your team to cross this line otherwise offside will be called. So dont skate towards the line and then decide not to cross it as the computer controlled players will have assumed that you were going to cross it, so if you then decide to cross the line offside will be called, unless you wait for those members of your team to come back over the line.
Icing
Is called when you clear the puck from one end of the ice to the other but the opposition touch the puck before yours. I'm not 100% certain but the puck has to cross 3 lines in order for icing to be called. If icing is called a faceoff will take place near your goal, so it best to try to avoid them, but sometimes you will just need to dump the puck down the ice for a breather.
Penaltys
If you bend the rules to much you will have players sent off for 2mins(usually) so your be left 'shorthanded' (4vs5) which isn't a good thing, if you commit another foul you will go down to 3 players, but not down to 2 if you commit another. There are various fouls but the most common in NHL08 are Roughing, elbowing and tripping, the latter 2 speak for themselves but roughing is a bit different. Roughing should only be called if you take 3steps(i think)toward the opposition(bit like travelling in Basketball) and then perform a bodycheck.
i cant really think of any others, but the more you play the more your pick up as the rules of ice hockey aren't that complicated really, although if you lookup the NHL rulebook on nhl.com the book is 312pdf pages long!