I am sure that you have heard your coach tell you to cover a certain player from the other team. You may have to cover a cherry-picker that is always getting breakaways, or you might have to cover a kid that will not stop scoring goals against your team. No matter what the situation is you have to realize that he is a threat. Even when you are playing man-to-man defense you still have to make sure that you are using these same principles.
To stop somebody that you have to cover you need to do things
1. Make sure you know what the other player will usually do
2. Be patient
3. Watch the eyes
Understanding the other player
If you have the chance then you should be watching the player you are being matched against when he is on the ice. Watch every move he makes and try to understand why he is making those moves. Check to see if he tends to go to the front of the net, the corner, or if he hangs back. By the time the game is over you should be able to tell what the player is going to do all the time.
Being patient is much easier said then done. Many players will just try to bother the other player to stop them from getting the puck, or being able to do anything in the game. However, the other player can easily breakaway and get an opportunity to score a goal. Instead you need to make sure that if he gets the puck he can not do anything with it, better yet, make sure that you can intercept any pass that comes to that player.
If the player you are facing has the puck then you need to give him the worst shot on goal possible. Do not skate directly at the player because he will be able to easily move around you and score. Instead force him to one side of the ice by skating backwards and make sure that any shot he takes can be easily stopped by your goalie.
Watch the Eyes
Watching the eyes of the other player is not something that you should concentrate on completely. Really it just needs to be looked at every once in a while, or when something important could happen. The eyes tell the entire story of what the player is looking to do. If you see him glance toward open ice, then you know that he is about to go towards the open ice, if you see him watching the puck, then you should realize that he wants a pass. A player will always look at what he wants.
If you want to stop the player that you have been matched against from scoring a goal, then you need to be able to understand what they are doing. You always have to know what they want to do, and when they want to do it. Always assume that the other player is going to take every opportunity to score, your responsibility is to make sure that he does not score in any situation.