Ax throwing has so many different styles: one handed, two handed, over the shoulder, over the head. I've even seen folks throw underhand. You need to find a way that works for you. I tried to teach my 12 year old son how to throw with no success at all. When another guy showed him a different style, he did much better.
I assuming that you know the basic rules and have the correct axe. If you need help there, let us know. I could try and describe the most common techniques, but the best thing to do is to take note of how the top throwers throw, and try to duplacate what they do. Also, my technique changes with the axe I use. When I use a heavier axe, I have to keep my feet closer together.
No matter how you throw, there are three elements that are constant. You must throw the same way every throw and you need to follow through on the throw. Most importantly, to me, is that you have to never take you eyes off the bullseye. Walk up to the the line, and just focus and concentrate on the bull. Try to stare a hole through the target with your eyes. Keep you eyes on it all through the throw, you should still be staring at the bull as you follow through.
Take note of you grip, foot placement and the position of the axe before you throw, and when you throw well, try to replicate it.
Try this: When you grip the axe, don't wrap the thumb on your upper hand around the axe, lay it along the back of the handle pointing toward the head. Keep you hands together like your'e holding a baseball bat.
Make a mark on your handle and use it to make sure that your hands are in the same place on the handles on every throw. Move the mark to experiment with hand placements until you find one that works, then mark it with tape or a marker.
It takes time. I practiced for 1/2 hour + per day, 4-5 day per week for months until I was good enough to compete. I've since won a (very) few bucks at some (very) small shows. Not suprisingly, the more I practice, the better I do.