Like a lot of knitters, I was intimidated by the concept of short rows until I did them for the first time and realize that they are not that bad. I've since used them on an Elijah, my Vivian sweater, and my Lightweight Mountains Peaks shawl. They are really not that difficult and are quite helpful in certain situations.
You work short rows by knitting part of a row, anchoring the yarn, then turning the work around and knitting back to the start of the row. This effectively lengthens one side of your knitting more than another, which is useful in a variety of cases. For example, in the case of Elijah, short rows were used to shape the ears; for Vivian, they were used to raise the neckline in the back of the sweater; and in the lace shawl, short rows helped turn the corner of the edging.
The key to short rows in anchoring your working yarn. If you do not anchor, you end up with a little hole where you've basically created a hard edge where there shouldn't be one. You anchor the yarn by doing a wrap and turn (w+t): knit the desired number of stitches, slip the next stitch with yarn in back,bring yarn to front and turn the work (yarn is in back again after turning), slip that stitch again, then knit to the end of the row. Basically, you've wrapped the working yarn around an extra stitch to anchor the yarn to the fabric and avoid creating a hard edge.
The real confusion about short rows comes from what to do with that wrap when you next encounter it. Techknitter gives a nice run down of several options of what to do at this point, so I advise you to head over there for the best explanation. For the purpose of this blog post, I'll highlight what I do with wraps in garter stitch: I simply ignore them. The wraps look like purl bumps and blend seamlessly into the fabric.
If you want to learn short rows for the first time, I advise you to start in garter stitch, so you don't have to worry about hiding the wraps. I recommend making a pair of Garter Stitch Mitts (that's the pair I just finished, above), which is a cute free pattern that uses wrap and turns to do most of the shaping. Once you feel comfortable with the 'wrap and turns', it won't be any problem to tackle other short row methods that hide the wraps in fabrics like stockinette.