Here is what I have learned based on 10 years of experience framing and matting my work. Most of the decisions boil down to ratios. Here are the general rules I use, most of which I learned from my local frame shop:
1) The width of the frame and the width of the mat should never be equal - typically the width of the mat is around 2x the width of the frame.
2) You can violate this rule if the frame and mat are the same color.
3) There should be some balance between the width of the frame and mat and the size of the photo - in other words don't frame a big photo with a skinny frame. The approximate ratio for smaller work (up to 11x14) would be to have the mat+frame equal around 1/4 the picture width. So going from edge to center of photo, there would be 1 part frame, 2 parts mat, and 6 parts photo. As the photo gets larger, the ratio would also get larger.
|1xframe|----2xmat---|------6x photo------><------6x photo------|----2x mat----|1xframe|
4) The mat should be the same width on the top and bottom as on the sides.(Unless an intentional offset is desired. In other words, don't have a 3 inch strip of mat on the top and bottom and a 1 inch strip of mat on the sides.
5) If you use 2 mats, they should never be equal width. Usually the second mat is inside the first, only around 1/2 inch wide and serves as a frame in a frame. And if you violate rule 4 and have the mat different widths around the frame, do not have the inside mat vary as well. It should be a constant width around the photo.
6) You can put a photo in a frame without a mat if the frame is wide enough to make the frame-to-photo ratio look okay. But professionals put a spacer between the glass and the photo so the two don't contact each other. (I have had photos stick to the glass - especially metal prints.)
7) The frame style should reflect the subject of the photo - or be neutral and let the photo do all the talking. I generally prefer black or white frames - especially since I have to swap photos in and out when something doesn't sell. But for the high-end pieces I find a frame that emphasizes the subject and mood of the photo.
8) If the mat is not a neutral color, it should ideally bring out some accent color in the photo - not necessarily match it, but help make it a bit more prominent.
Note that all of these are rules that generally make the presentation aesthetically pleasing. If you want an edgy look then do something different - like offset the print into a corner, use a contrasting color for a frame, etc.
Hope this helps.