The biggest issue with starting any kind of photography business, in my opinion, is experience. Especially if we're talking weddings. My photography skills have improved over the past year and I'm looking to add weddings to my portfolio, but I know that I am not a wedding photographer (yet). And I am not going to possibly ruin some bride's big day by claiming to be something I'm not.
So my strategy learning wedding photography is to make sure I get myself invited to weddings of everyone I know. I shoot pictures, but I make sure I stay out of the hired photographers way. If possible, I try and buddy up to the photographer to see if s/he will answer questions. I watch the photographers and take notes. Where they position themselves, what equipment they use, etc...
I have shot two weddings myself for friends, but I told them up front that they were better off hiring a wedding photographer and I'd only do it if they couldn't hire one (couldn't find one for their date, or couldn't afford one) and I made them look at my existing portfolio to see what my style of shooting was. Fortunately, in both cases, the bride was happy with my work. I have two more weddings I'm doing this year, again as favors, and then I think I'll be ready to actually add it to my services.
I have tried to offer my services free to a few local wedding photographers in exchange for learning, but this is not a good time for that. Even a few that I am friendly with are leery of letting someone else into the business. Two years ago there were 5 wedding photographers in the phone book, this year there are 31. Most of them don't have a web site to view their work and when you talk to many, they've never actually shot a wedding professionally.