As with the shot put, throwing the discus also has 3 Basics Steps.
Step # 1, The Grip and Release: Holding the discus is a very important part the process. To hold the discus, I suggest that you take the discus in your non-throwing hand, then with the index finger of your throwing hand, find the middle of the rim of your discus. Place the tip of your index finger just over the top of the rim. Next, turn the discus so that the rest of your fingers are just over the edge of the rim of the discus. The thumb should ride on the plate of the discus, just as if normally placed next to you index finger (it's too short to reach the rim). So you should have the 4 fingers of your hand just over the rim spread evenly apart, with the thumb riding on the plate of the discus.
Now if you turn the discus so that your throwing hand is face down, holding the bottom of the discus in your other hand, this would be the correct throwing position of the discus. If you drop your other hand, the discus should fall down. To keep the discus in the throwing hand, you'll have to use centrifugal force. While holding the discus towards the front of your throwing area (right handed throwers, to the left of your body; left handed throwers, to the right), try to swing the discus back to the other side, releasing your bottom hand, then swing the discus back to the throwing area and catching the bottom of the discus with your other hand.
You'll need to do this several times before you'll get the hang of it, but you'll get it. What you're trying to achieve is to keep the discus in your throwing hand by using the centrifugal force to keep it in your fingertips. Once you've achieved this, you're ready to release or throw the discus.
#2) The Balanced Power Position: You've probably heard the term Power Position in almost every educational writing about throwing, whether it be the shot put, discus, hammer throw, or javelin. I'd like to include an additional part of the Power Position, called Balance. The Balanced Power Position is very vital to the throw of any implement. Many throwers either glide or spin into the power position, unbalanced. This will have them throwing off balance. If you notice something similar to some of the positions in shot put and discus, they have a lot in common with ballet. Your finish position is somewhat of a pirouette in ballet. So ballet is an art of balanced positions, so is shot put and discus. You must get to a balanced power position.
Feet a little wider than shoulders width, back foot bent slightly to get your angle, shoulders square to the back of the ring, with the weight over your back foot and balanced (not too much to the right or left, right over the back foot). Once you're in this balanced power position, you will find it easier to throw far, because it makes it that much easier to explode or whip through the throw. Now just like above, you'll need to practice getting into the balanced power position and throw, and throw and throw. Note: The way you get height in the discus and shot put, is to bend the back leg. The more you bend it, the more height you'll get. We want to pull the discus across our chest area to throw, this is where all your muscles are. If you try to stand straight up and throw by raising your arm to get height, you'll notice that you're losing power, the higher you raise your arm. Remember your muscles are across your chest area, bend the back leg to get height.
#3) The Stand Throw: The Stand Throw is the most important part of your throw. This is the main portion of the throw that accounts for about 85 to 90 percent of your distance. Now, standing in a balanced power position, get down on your back foot by bending the knee. Swing the discus back into a balanced throwing position and with the opposite arm and side of your body, start pulling towards the throwing area and begin to start elbowing. As you near the throwing position, close your opposite elbow and start pulling the discus through the release point. The discus should be released in the release point which is about 90 degrees from the front of the ring. If you release it too early, the discus will tend to go outside of the sector.
If released to late, it will tend to do the same, so try to release it in the middle. Now the releasing of the discus or shot put for that matter is done in the air. As you swing the discus forward, you should be pulling the front side and driving the backside forward simultaneously as you're pushing the back leg to lift you off of the ground. While you're turning in the air (TITA: Turning In The Air) you are pulling the opposite side around by elbowing and pulling the discus through the release area, releasing the discus in the middle as you're driving the whole body up and out and all the way around. Now work on these three parts of your throw and you should be on your way to throwing as far as you possibly can.