Anyone know how to catch a paddlefish?

Paddlefish are filter feeders, so they can't be caught by usual fishing methods.  Some people spear them or snag them by accident.

The Classic Michigander 

I've heard of the occasional paddlefish sucking up by accident a baited worm or minnow. However I've only heard of mostly snag fishing for them.

ok, thank you.

Here in MO Paddle fish (or spoonbill as we call them here) are caught by snagging. We use huge treble hooks with heavy (6 - 8 oz) sinkers. We use snagging rods (like a surf casting rod) and catching them is a matter of casting out and horseing the hook and weight through the water until it "snags" them. It is a tremendous amount of work but the pay off is worth it. I have caught 30lb. spoonbill quite a few times.

In SD we have two seasons, in July there is an archery season which you must keep the first one you shoot. Then in October is the snagging season, you can keep one fish but all between 35 - 45" from the corner of the eye to the fork in the tail must be released. Archery is a real challenge you can either sit up by the dam and wait for one to surface close to you and try to hit it or you can go down river and run aroung the sandbars and spook the fish and the come to the top for and second and you have to try to make a quick shot. Snagging is pretty simple, use a 2/0 trebble hook and 3-4 oz weight throw it out and jerk it, can catch alot of fish in a day.