Depends on whether you put the long side or short side down. It the picture is 8"x6", an 8x10 inch frame will probably leave 1" of matting on all sides. Most frames that you put pictures in come with simple matting. You can trim it to size with something like a exacto knife or a razor blade. Most of the time, things like posters or certificates (diplomas and similar things) are framed without matting. It's also a matter of taste.
If you are going to have it done professionally, bring the picture and look at with the type of matting and frame you plan to use, and decide on the size while looking at it. That can be pricey, though. There are do it yourself framing places in most large cities I've lived in where you can do it yourself. I got lazy, and picked up some right angle framing clamps, and with the use of a mitre saw and router that I already have, made the last couple of frames I needed for simple jobs. I just buy glass. You need some tools and basic skills (a drill press helps too, I've found) to go that route.
If I'm not too ambitious, I can find a reasonable frame at Walmart. That's the way I put up kitten pictures over a litter pan (lots of people have baby pictures in their john, so, why not?)