First and foremost you want to find a photographer that is passionate about weddings and this is 90% of their business specialty. Ask them why they love shooting weddings. Their answer will help you determine if they are as excited about all the small details of you wedding as you are. Passion is huge!!! If they don't love it then it's going to reflect in the outcome of the images.
Secondly, a wedding photographer must have the knowledge of their equipment and the experience of wedding day flow... Wedding photography, in my opinion, is the highest level of photography that one can excel at. The reason I say this is because the photographer has to know every possible lighting situation, posing, composition, wedding etiquette, etc. all in a split second.
Questions that you can ask them to get a better idea of their fit for you and your special day.
Can they successfully mix ambient light with off camera flash?
Do they know their equipment and do they have back up equipment?
Do they work with off camera lighting?
Do they LOVE weddings? Are they inquiring as to the details of your wedding?
Are they making recommendations as to time scheduling based on their experience with previous weddings?
Can they show the highlights of a complete wedding?
How many weddings do they shoot a year?
Is this a full time job for them or a hobby?
Do they work with a consistent team of professionals?
Determine which photographer is the right fit for you. Get that emotional connection! Price is relevant, so consider if your hiring a "smart car" photographer or a "mercedes benz" photographer. Happy Hunting!