So this is hard to explain, but essentially, you place the headlamp into the headlight ring of the bucket...then, the clips's mid-section catch the outer edge of the headlamp, and the clip's "elbows" go into the front edge of the headlight ring. Next, with a screw driver or pliers, bend out the "open ends" of the clip and maneuver them so that they go into the opposite lip of the headlight ring (back part, closest to the bike). They'll snap in and the tension essentially locks the headlight to the ring.
You can usually place one or two and then put the headlight in, then do the remaining two...might be easier.
Here's a pic I found on the web with what they should look like: