I used to work in a big hotel which regularly hosted 5 or 6 weddings a week in the wedding season (summer). A great way to get into the scene is by leaving your details with the hotel, and suggesting the hotel offers prospective customers your details telling them they'll get a "discount" if they book the hotel's recommended band. Then you've got them interested in your stuff and you can give them a "discount" price, which is actually your normal fee! Then take off a small premium for the hotel's recommendation and give them their cut and you're good.
Most of the best bands in the scene are hired by word of mouth, so all you need is one good gig to get some repeat performance. It's breaking into the scene and getting a gig as a wedding band in the first place that is the toughest part, I suppose.
Going to wedding events is as good a way as any, but you'll need to give it a hard sell or produce something which really grabs the punters, as the pro wedding bands do pretty well to monopolise these events! If you're dabbling your feet in the water, it probably won't be the most productive avenue. Try getting on Facebook and find a friend or family member who is getting married, and play the gig for free. Take some photos, some good video and use that as an advertising platform.
You just have to try your best to be professional. The best band I've seen play at a wedding (Bass player is a member here, Mike if I recall, played a lovely Pentabuzz, a Spector and a Marcus Miller 5 string...) never wore suits to the gig or anything but looked like a pro outfit, were as tight as hell and could fairly play, but knew they were hired to play the typical cover tunes. If you can put on a good show and dedicate yourself to the market, you can do quite well locally.
That said, I've seen some bloody crap bands playing at weddings. A "revelation" it was not....!