Double Crochet (dc) and Triple/Treble Crochet (tr)
To increase one stitch at the beginning of the row in double crochet, work a double crochet into the first stitch of the row. Remember that normally you start in the second stitch of the row because the chain-3 counts as the first stitch of each row.
Here is a video demo.
You would work a triple crochet increase in the same manner as the double crochet increase, except you would make a triple crochet.