As they say " a picture is worth a thousand words". Which is why videos are a wonderful tool to learn from, especially for this topic. As I film them I will be making videos available with each finning style. Till then enjoy the descriptions.
Flutter kick: A powerful kick that uses the upper legs while keeping the legs fairly straight. If you are in proper trim (remember knees up) the energy from this stroke can be directed slightly behind, however it is very easy to stir up the bottom with this finning style and the majority of the energy is easily directed downward toward the bottom.
Modified Flutter Kick (aka "shuffle kick"): This kick is good for confined areas (swimming thru a narrow channel) and where you don't wish to stir up silt as the power from this kick is directed almost entirely behind the diver, not down toward the bottom.
Frog Kick: Same leg motion as for the breast stroke. A powerful kick that avoids silting and is great for conserving energy while moving at a steady pace.
Modified Frog Kick: Same motion as the Frog kick, but it's all in the ankles. Great kick for very precise movements and if you need to move slowly, or avoid bumping someone next to you.
Dolphin Kick: Uses the whole body in an undulating motion. Popular with breath hold divers. While this kick can move you faster than any other it consumes large amounts of energy and if done near the bottom will likely stir up plenty of silt. This can also be a good kick for when you just want to use some new muscles and give the old ones a rest.
Helicopter Turn: Useful for pivoting in either direction without stirring up the bottom. Move your feet in an egg beater motion, reverse to go the other direction. Takes practice, but is a handy manouver when you just want to look around. Also great for video footage as it allows you pan the scene very steadily.
Backward Kick: Next to the Frog Kick probably the most useful of the kicks. Allows you to back up slowly, which is great for photographers and when you don't want to bump into something (like that spiny sea urchin you are heading toward)