1) WATCH THE REFS HAND!!! That is by far and away THE most important part. As soon as you see a motion, swipe. You might have to go before he makes a move if you are up against a good face off guy but going on pure reaction when the ref moves his hand will do against most centers.
2) Once you get comfortable reaction time move your hands down. I'm talking half way (top hand) and 2/3s (bottom hand) down your stick. This will let you move the bottom of your stick faster since you now use more wrists instead of elbows to win the draw.
3) There are two ways to hold your stick. One way will win it to your forehand side (hold your stick normally). The other way will win it to your back hand side (bottom hand turned over). I suggest using the second method as it's easier to win it to your defense that way and winning it to your defense is better than to the wings.
If you lose a draw, don't panic, start back checking and play some D to cause a transition.
nice tips. If I'm doing bad faceoff wise through the game, sometimes I will try to box out the other guy to change it up. Another one is if its a defensive zone draw, you can push the opposing players stick real hard and force him to draw it back too far, out of the zone. That one can make you look foolish if you're not good at it though, but it's another thing.
There's also several ways to read the opposing centers body to tell exactly what he is going to do, but I'm not too good at that. Maybe someone else can touch on it. This I would assume can help you decide if you want to try and box out the player (if he's presumably going forward and through you I guess) or if he's trying to win it clean back, etc...
You do want to take those tips above and use them according to situation. Don't try to win it on your backhand if the puck will wind up in the slot in your defensive zone cause the other team will take advantage of that or your goalie might fall asleep and let one get by him.
One thing I find that works is to keep my blade kinda twitching...I keep it moving enough so I can anticipate the refs hand but not enough for him to kick me outta the zone. I liken it to skating where you wanna keep moving or you might get caught flat footed. It helps your reaction time a tad bit is all I'm trying to say.
I would add that if you are having a hard time winning, your initial goal should be to not lose it cleanly.
First look to see which way the other C is going with the draw, and just go right for his stick before he can get to the puck. It will become a battle of who gets their skate on the puck quicker. Figure out which way he is going with his stick based on hand positioning, and just go right for the shaft of his stick when the puck drops. This doesn't work every time, but is a good strategy to use once in awhile, especially in the defensive zone.
Second, as Lotus said, never draw the puck back to your own goalie in the defensive zone. The easiest thing to do is just swipe the puck on your forehand towards your winger along the boards.
If you are having a hard time drawing the puck on the backhand, I would suggest turning over your bottom hand and sliding your top hand down a bit to get more leverage. Otherwise, just look to win the puck on your forehand and draw it towards the wing/D-man on your forehand side.
My only other advice is don't forget about the opposing C after the puck drops. You don't want to win the puck back just to have him walk right around you and gain possession.