Sponsorship varies from club to club.
As stated above, go to an event open to non-members. Most Clubs that have Trap or Skeet are open to non-members when they shoot. If not, they're likely to have the gate unlocked, at least. Go talk to a few members, tell them that you're interested.
At my Club (not in your area, sorry) we often have potential members show up at Trap, chat for a bit, maybe shoot a round (lets us see if you're safe), and take an application with a couple sponsors' names on it. Either that, or show up at a monthly meeting. I'd advise talking to some Members, before you get too "into" a Club - each place has a "vibe," and you may want to make sure that you're compatible.