Throwing a cast net is just like learning anything new. It will be a little shaky at first, but with a little practice you'll be throwing that net like a pro every time. The key is practice. Practice throwing your cast net in the yard at home. The following instructions are assuming that you are right handed. If you are left handed, just do the opposite.
Make a wrist loop in the end of the hand line and place it over your right wrist. Then make a number of loops in your right hand collecting the hand line.
Check the draw strings to make sure they are hanging straight. Then grasp the entire net about 1/3 of the way down.
Grasp lead line in both hands and check it to make sure it is not twisted or tangled.
Make a smooth, full counter-clockwise turning cast. Practice in the yard will help you get the best results. Distance will come with experience.