When: Sundown every Saturday and Sunday. May start as early as noon. It will often happen any day of the week during the summer. By sunset, it will be in full swing in the middle of the beach.
Where: Breeze Ave. or Brooks Ave. meets Ocean Front Walk.

The drum circle starting at Brooks and Ocean Front Walk:

The drum circle after it moved to the middle of the beach:

As far as I can tell, no one officially runs it. There is no rhythm leader and if you're drumming along, you've got to find your place in it. The vibe will likely be different every time you go.
Here's a youtube video from about 17 years ago. It's still the same. There are cop cars in the video, but they don't show up that much.
Another video of the drum circle at Brooks and Ocean Front Walk before it moved to the beach.