Contact the show secretary & ask for the entry form & show booklet.
The rules specific to that show as well as any premiums or prizes will be listed, along with entry deadline and other pertinent information.
Prize money is not common, but is more often found at fairs or breed club nationals.
I've never seen a show where club membership was required to enter, although for some prizes you must be a member (for example, APA & ABA awards require membership; breed club awards and prizes often are limited to breed club members). Most APA or ABA sanctioned shows are open "to the world," but some fairs and some states limit entries to locals,