I do several things to win faceoffs. I agree with the advice that you have to have a mix of techniques to change up things and keep your opponent off guard. I have several techniques that I'll share.
1) Backhand sweep - Keeping eyes focused on the puck in the official's hand, you set up with the toe of your stick on the near right corner for a lefty or near left corner for a righty of the faceoff circle and push out across the dot and then sweep back through the dot as the puck is dropped timing the sweep with the point where the puck is hitting the ice. A tip that I found and mastered over time was actually picking up my stick as I swept back about a 1/2" off the ice to add that 1/2" to the width of my stick blade as it came through the dot to increase my odds of getting the puck. Takes a lot of patience, hand-eye coordination, and practice to master this technique.
2) Slap and pull - Eyes always should be on the puck in the official's hand. As the puck is released, I quickly swing across the circle and slap the opponent's stick shaft about 4 to 6 inches above the blade and effectively block him from moving his stick forward until the puck settles on the ice where you can then release and pull the puck back as you wish in one motion.
3) Block and pull - Much like the Slap technique, I use this against opponent's that are weak on their stick and looking to simply push their stick forward, turn the blade, and sweep back across along the ice. As the puck is released, I push the blade of my stick quickly across the dot as the opponent is moving forward and before they turn their blade. The face of the blade of your stick should meet the toe of your opponent's stick and block his stick from having any access to the faceoff circle. Again, when the puck hits the ice, I will release my block on their stick and pull the puck back in whatever direction I wish as I have inside positioning on them and they cannot get to the puck or block my path without picking up and repositioning their stick.
4) The Wall - I typically use this when I'm not sure of their strategy. The technique is known as building a wall, because you are going to put all of your body weight down on your stick as you reach across the dot. As the puck is dropped, you push your stick blade (face of the blade pointing straight ahead so that it's as wide as possible) across to the far side of the dot and lean down on your stick as your read what you're opponent has done. If they have tried to come low, you'll generally block them out of the circle. If they have picked up their stick or gone around your stick and now have inside position though, you are going to hold firm and build a wall to prevent them from winning the puck back. If they have gone around your stick low, the shaft of their stick is usually blocked by your stick and provides them no leverage as you block their attempt to win the puck and then pull straight back. If they have picked up their stick over yours and have their shaft and blade inside of yours, again you will hold firm on your stick to block their attempt to win the draw back and then use your leverage down on your stick to win the puck back in the process pulling the puck underneath their stick by using your weight down on your stick to use the rocker at the base of the heel of their stick to effectively create a ramp.
Unlike techniques 2 and 3, The Wall technique does not control your opponent's stick and therefore is vulnerable if your opponent looking to move the draw forward and step around you.
Those are my main techniques. Always watch the puck at all times. Keep watching it from the time it is presented in the official's hand to the time you win the draw to your teammate(s). Last note, any time I miss the puck on my first attempt at it, I will immediately seek to recover by lifting or pinning the opponent's stick. Once the puck settles, if I can get to it first I will release the opponent's stick and win the draw or if it is bouncing or my stick is not free, I will use body positioning to shield the puck for my teammate to come in and take it or kick it a teammate.
You definitely titled the thread correctly. Taking faceoffs is truly an art form. Everyone is different, but when you can master a technique, it really is a beautiful and handy tool to own...