Increasing seems to be more frequent in crochet than it is in knitting. Fortunately it is very easy.
To increase you need to make a new single crochet in the same stitch that you just used. This will result in two stitches coming from 1 stitch.
After completing a single crochet put the crochet hook back through the same stitch. Then follow the same steps you would normally use for single crochet.