Stockinette, or Stocking Stitch, as its called in some parts of the world, is so basic that most patterns don't explain what it is or what they mean when they want you to knit it — chances are that you are already well on your way to doing it.
When you first learn to knit, you learn the knit stitch, and when the knit stitch is repeated for every stitch of every row that gives you Garter Stitch.
Once you have that down you'll learn to purl.
If you purl every stitch of every row you also get Garter Stitch, but if you knit one row, purl the next and repeat that pattern, you'll end up with the most classic of all knitting patterns, known as Stockinette Stitch.
Knitting Stockinette Stitch
If you were to write out a pattern for Stockinette Stitch, it would look like this:
Row 1: Knit.
Row 2: Purl
Repeat these 2 rows for pattern.
Stockinette Stitch works on any number of stitches.
You might see Stockinette Stitch abbreviated in a pattern as St st.
What Stockinette Looks Like
The "front" or "right" side of the fabric will look like a series of Vs, while the "back" or "wrong" side looks like a bunch of bumpy ridges.
Pros and Cons of Stockinette
Stockinette is a great knit fabric because it's simple, easy to increase and decrease in because you can't mess up the pattern, and it gives you handknits that look like many classic machine-knit, store-bought pieces.
It knits up pretty quickly because you're repeating the same stitch across the row, and once you've had a little practice you can knit it without paying much attention to what you're doing.
It's also a great backdrop for embellishment. You can, for instance, easily add stripes to a project worked in Stockinette Stitch without changing the gauge. You can also add designs with duplicate stitch after the knitting is done, or embroider or add beads to make the project more interesting.
One of the perils of Stockinette Stitch is that it tends to curl when left to its own devices. Some yarns show this tendency more than others, but it's a fact of the structure of the stitch that you can't always predict.
You can counteract the curl if you want to by adding a border of ribbing, Garter Stitch or another non-curling pattern to the edges (as in the washcloth linked above) or use the curl as a design element.