What is the most cost-effective way to frame a photograph or art print?

It depends on how much you value your time, of course, but using a ready-made frame (like those from Ikea) and cutting your own mat is not rocket science. You can also order custom-cut mats from places online. Keep in mind that the mats and backing boards in many ready-made frames (like those from Ikea) are not acid-free, so they will discolor and also potentially "burn" your photograph. And the glazing will almost certainly be regular glass or acrylic, not anything that offers any sort of extra UV protection. And don't forget to use an acid-free tape to attach your photograph to the mat.

You might want to try http://www.pictureframes.com They have a good selection, will cut to custom sizes, and will cut custom matting if you want.  I've used them for years and haven't had a complaint that wasn't quickly addressed.  I do cut my own mats but as mentioned already the good machines are expensive. Another more recent option is to go frameless.  Bay Photo and others have wall collages and other affordable options for a nice, clean wall arrangement without frames.  I'm considering taking some of my framed photos down and replacing them with these.  Just a thought...

I don't know ... just to play devil's advocate here ... if you are talking about cutting your own matte with an Xacto knife, fine, that is easy to do yourself but not if you want a bevel. If you want a bevel you need a matte cutter, and good matte cutters are actually expensive. You can buy a cheap matte cutter but I don't recommend it. So my answer to the original questioner's question would be, generally, that it depends on how nice a frame job you want. If the photograph is a standard size (which it probably is) then by far the easiest thing to do is buy a frame with preincluded matte from wherever. If not then buy a frame and cut your own matte with a craft blade and do without the standard bevel. Otherwise, find a discount framer.

You can use foam board to frame your photo graph or anything you want. the foam board for framing your picture would be acid free foam board. It creates a acid free barrier between artwork and mounting board. The surface of the board is completely acid-free and buffered to maintain a neutral pH level. The core of the material is also chemically inert. It has all the qualities of a regular foam board, including weight and moisture resistance. You can read all the information related to foam board. http://blog.foamboardsource.com/2015/06/the-best-foam-boards-for-framing-photo.html.

Rather than have printing and framing of your photograph or art print done in separate shops, be cost-effective by having it done in only one place. Some shops give discounted packages if you have this dual service done by them--some would even throw in the cost of the frame for free for big photo printing jobs. Check out such offers to generate unexpected savings.

Michael's and others sell a variety of frames and mattes. They fit a number of price points. You can also have the custom cut a map or frame for you as well.