Making a yarn over is a simple way to increase stitches. Using a yarn over makes a hole in the knitting and is popularly combined with a decrease such as knit two together to keep the number of stitches the same across the row.
To make a yarn over between two stitches, just wrap the yarn around the right-hand needle from back to front counterclockwise before knitting the next stitch. Then just work the next stitch as normal. When you get to the yarn over on the next row, treat it as a regular stitch.
Working a yarn over is the same whether you're knitting or purling the next stitch. When knitting you wrap the yarn around the needle and leave it in the back; when purling, wrap it all the way around the needle so the yarn is back in front where it needs to be to purl.
Learn more about yarn overs for different situations.