As someone who is fairly new to orchids, but who is a member of many hobbyist clubs (amateur astronomy, tropical fish keeping, aquatic plants, home tissue culture, etc.), I can say you've already received great advice, particularly about being friendly and welcome to new members/guests that show up at the meetings.
I think you've also realized that recruiting new members is crucial to keeping any hobbyist club vibrant. Places like OrchidBoard are great for letting people know you exist. I saw your club's website link in your profile, and visited, but it looks like it hasn't been updated in a long time - make sure your website is up to date. It gives people the impression you are a vibrant and lively club.
Make up flyers and distribute them in local nurseries that grow or sell orchids. Or even in your local big-box hardware stores, who seem increasingly to sell inexpensive Phal hybrids. "Want to learn how to keep your orchid in good health? Join the Northeast Alabama Orchid Society!" That kind of thing. Sure, you'll get a lot of folks that will come once and never be seen again, but you'll also get a few folks hooked and coming back for more (hehe, why does that sound like we're drug dealers?
).
An example: I would not have known there was a relatively local Orchid Club unless I had seen on the FirstRays website that he was giving a talk in Wheaton, MD this last weekend, at the Brookside Gardens Orchid Club meeting. After a little investigative work (they do not have a website, only a Yahoo group), I attended the meeting with my wife. We were warmly greeted as we walked in the door (though perhaps it helped that we had a box full of Paphs we had bought an hour earlier at Woodstream Orchid's open house
, and we were off and running. We had a great time, and while BGOC is obviously a small club (there were about 10 people there), we went ahead and joined and will attend future meetings.
Oh, and I like the show and tell idea, too - when you're new (and perhaps even after you've been doing this for years?), there is such a bewildering variety and diversity of orchid species and genera that I bet you could do 5 plants a meeting, and go a year before someone brings a plant you already have. It would be a great learning opportunity.
Anyway, good luck, and try hard to keep your enthusiasm and passion at the forefront - the effect will wear off on everyone!