Be sure to view samples of their work and not just hightlights and trailers. Whenever possible, ask to see at least one entire wedding as it will give you a better idea of the overall quality and style of their work.
Ask a trusted professional you've already hired for a recommendation such as your Wedding Coordinator or Photographer. Find out who the other professionals you trust and you respect are recommendding. In most cases they will be recommending someone who is talented, likable and ethical because if you have a bad experience it will reflect poorly on them.
Make clear to your videogapher what your priority is: Capturing family and friends, focusing on you and your fiance or a combination of both. Trust their experience and artistic vision and keep your request simple. It isn't about asking them to itemize every shot, but rather you're giving them a sense of what you would like the focus of your finished video to be.
This should be a red flag:
Pay attention and make sure that the videographer is writing these notes down. If they aren't writing it down they are very likely not going to remember what you said by the time your wedding day arrives. You may then end up with a finished video that focuses on an aspect of your wedding that wasn't a priority to you.
Ask who will be editing your video. Will it be the same person who edited the video sample you saw that made you want to hire this particular company? Will the editing be done in house or by a sub-contracted company? Some videographers sub-contract their editing out to specalists who will do a great job editing your video. Others will send your wedding out to an editing company who focuses more on low price and volume rather than quality. As with all things, being aware can help protect you from companies that cut corners leading to disappointment later on
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Ask how long it will take to receive your finished video. This touches on a misconception people may have about videography that the bulk of the work is shooting the video on the wedding day. In actuality the editing typically takes many more hours than the shooting. Because of this it can take months to receive your video back. If the timeframe is important to you be sure to ask videographers you're considering hiring what their turnaround time will be.
Clarify if they will be bringing an assistant(s) on your wedding day and what this person's qualifications are.