There have been a number of articles posted on the web on this topic, so this is just my personal take on the subject. The most common initial factor people consider is budget. Weddings are expensive, but you get what you pay for and wedding photography is no exception. Expect to spend at least 10% of your total wedding budget on the photography, less than that and you are taking a risk. While the flowers, the food and the DJ are all very important, what's left after the day is over and you are back from honeymoon is your marriage ( hopefully! ) and the photos.
The next factor that comes into play is style. There is still a lot of very traditional wedding photography out there for those that seek it, with a focus on posed shots and the dreaded group shots..
The new hot style these days is documentary or reportage wedding photography. This style seeks to interfere with the day as little as possible and adopts a purely documentary approach.
There is of course a combination of both and these days the fashion industry is having an influence on some photographers, leading to some very interesting editorial style images.
Personally, I love the documentary approach but I also see the need for some of the traditional group shots, and I have strong ties to the fashion industry ( I shoot for fashion agencies and also teach fashion photography ). I like a mix of all three with the emphasis on whatever my client prefers.
A third factor that should not be underestimated is how well you get on with the photographer. There has to be some sort of connection, you will be spending a lot of time with this person on the biggest day of your life, so it needs to be someone you are comfortable with. This can be established with a phone call or skype, but I prefer a face to face meeting if at all possible ( sometimes distance does make this difficult but I will always make the effort to at least meet you halfway ).
Point four - gear. In many areas of photography gear is not that important compared to the skills of the photographer. Wedding photography is not one of those areas of photography, gear really is important. You need professional lenses to operate in tricky lighting conditions, gear that is weather sealed in case it rains, and backups for your backups. Many of the cheap photographers out there only have basic gear with no insurance and no backups, stay clear of them if you can afford it.
Lastly, try and see a full wedding shoot from your photographer, this can be in the form of an album or a video slideshow reel ( I've got several of these on this site and its a great way of seeing how a photographer has captured a single wedding ). If the photographer only has a best of collection of shots on their site its likely they have only been an assistant or second shooter.
Hope this all helps! Good luck with whomever you choose to capture your wedding!