Increasing: The Single Yarn-Over

The simplest way to add a stitch to a row of knitting is with a single yarn-over (“yo”).  When the yo is subsequently knitted or purled (on the return row), it leaves a hole, which you want if you’re making lace or eyelet, but which you should try to minimize if all you’re after is a simple increase (see reverse yarn-over, cross right; and reverse yarn-over, cross left).  

To make a regular yo . . .

when the next stitch is a knit:

Bring the yarn forward between the two needles, wrap it over the right-hand needle, and continue working with the yarn in back.

when the next stitch is a purl:

Bring the yarn forward between the two needles, wrap it over the right-hand needle, and bring the yarn forward again.  Continue working with the yarn in front, as for a purl.  This leaves a slightly larger hole than a yo between two knit stitches.

at the beginning of a row:

When the first stitch is a knit, put the right-hand needle under the yarn and proceed to knit.

When the first stitch is a purl, wrap the yarn over the right-hand needle and bring the yarn forward, then proceed to purl.

in garter stitch, use the reverse yarn-over:

Instead of bringing the yarn forward between the two needles, begin with it at the back of the right-hand needle, then bring it forward over the needle and to the back between the needles.  Continue knitting.  This leaves a smaller hole than a regular yarn-over.

cross right (stockinette):

Create a reverse yarn-over on the knit row, then when you reach the created stitch on the return (purl) row, purl off into the front of the stitch.  This will make the stitch cross to the right.

cross left (stockinette):

Create a reverse yarn-over on the knit row, then on the return row, purl into the back of the stitch.  This will make the stitch cross to the left.

The cross-right and cross-left produce a close stitch, with no eyelet.  Used as a pair (say, on either side of a gusset), they give a smooth, flat seam.

Tomorrow, the bar increase and moss increase (making two stitches out of one).