Two simple and common methods of increasing a knit stitch are to knit into the same stitch twice and the simple yarn over technique. There are several ways to increase a knit stitch, depending on the desired effect.
Knitting into the same stitch twice is called a bar increase or a knit one front and back, abbreviated as kfb in written knitting patterns. This increase produces a solid fabric with a small horizontal "bar" underneath the added stitch. To make a bar increase, first knit into the stitch as normal, but do not slip the stitch off of the left needle. Instead, enter the same stitch again from the back so that the right needle points from right to left. Knit the stitch again and slide the stitch off of the left needle. This increases the stitches in the knitted piece by one stitch.
The yarn over increase, abbreviated yo in written patterns, creates an extra stitch and an intentional hole in the fabric. The yarn over is commonly used in lacy patterns or as a simple buttonhole. To make a yarn over increase, move the working yarn between the two needles, and then under and over the right needle so that it is back in knitting position. Knit or purl into this loop of yarn on the return row.