Consistency Is Key
Proper technique in darts grows out of a comfortable stance, which allows you consistency in your throw.
The best players throw consistently on all three throws.

Take a Stance
Begin with your right foot forward (left foot if you're left handed), touching the throwing line.
Ideally your shoulders should form a 90-degree angle with the dart board, but for most people somewhere between
50 and 80 degrees is more comfortable. Most of your weight will go on your front foot, with just enough on your
back foot to balance. Keep your grip firm but not tense.

Got Grip?
Different barrels will require slightly different grips: Longer barrels allow more fingers; shorter ones allow fewer.
Keep your thumb behind the dart's center of gravity.

Focus
Line up the target and dart with your eye. Stay focused on the target, not the dart.
Try not to move your body during the throw. Even your shoulder should stay stationary, letting your arm do all the work.
Once you have aimed, bring your arm back and accelerate in one smooth move.
Don't force the acceleration, let it occur naturally. Don't allow the dart to point down at any point during this movement.
You will feel the optimal point to release the dart. Allow your arm to follow through and end with your hand aiming at the target.

Comfort Zone
The most important point is to find a stance and grip that are comfortable for you.
If you're not comfortable, you won't throw well. Practice and experimentation will help you find your best technique.