I basically agree with Roger; with a small caveat.
The image comes first; the size that it is is the size that it is!
Then; I typically want (hopefully) no less than 3 inch of mat around each edge; and I'll try to "end up" at a standard frame size to make it easy for folks to have it framed. Once again; I don't do this professionally, so this is just my opinion.
Start with the image size.
Ensure you have at least 3 inches on each border.
Move up to the next highest "standard frame size".
And cut mat's and backboard to match.
So an example of this might be:
Printed image size: 14x21 image surface with 16x23 paper size.
So if I add 3 inches to each short edge (3"x2=6") and add that to my image size (14+6=20) I end up at 20.
If I add 3 inches to each long edge (3"x2=6") and add that to image size (21+6=27) I end up at 27.
So I need a frame size of at least 20x27.
Then looking at standard frame sizes I see that a standard frame size is 22x28. By then basing the my mats on this frame size, I end up with *roughly* 4" inch mat and a 3.5" mat.
When cutting double mats, you do need to stay focused on the math lest you make a mistake! Since I overlap my image by 1/4 inch on all sides; if I'm off by a 1/16 or so; not too big of a deal. Ken pointed me the way to his "matboardcalc" spreadsheet which should do everything ones needs. And yes, sorry, but I too am not so great with math and appreciate the help a spreadsheet offers.
"For me the question isn't about the mental arithmetic, but rather how precise everybody is with their images, frames & mattes."
Well, from my point of view, I like to let the image determine the matt and frame sizes and not the other way round. So if things come out in fractions of a cm, so be it! That's why I find the software so useful.
If I stuck to, for example, 16 x 12 inch prints then I'd buy standard matts and frames.