One of the most frustrating exercises for people learning Kettlebell training is the Clean. Bruised wrists are no fun and the Clean can bring them on - so here are a couple of tips to clean it up. (just can't help the puns)
First cheat curl the KB to the rack position (use your left hand to assist the bell to the right shoulder for example) - get comfortable with the rack position (your thumb should point toward your shoulder). Second - when you drop the Kb to hike it behind you your upper arm stays glued to your ribs and your thumb will point behind you. Third - when you perform the hip snap to bring the KB back to the top - your upper arm stays GLUED to your ribs and your thumb rotates back to pointing to your shoulder.
What should happen is the KB will have a very short or "tamed" arc and the KB will come around the wrist and arrive gently at the top. Remember that the hips are still the mover of the KB and it is not a curl and even though the hips still finish they don't need to put the same energy into the clean as they do the swing.