All you need to know about clay pigeon shooting in a single guide. I'm pretty sure you had no idea Saints Row: The Third offers such a thing, but I assure you it is real.

Find a potential target, and take it as a human shield.

After that you will have the target in this position:

Once you are holding the target just throw it in the air.

All you have to do now is shoot the target, with a weapon of your choice (shotgun recommended).