The double crochet (DC) is the base for so many other stitches. I will explain how to simply work it in rows.
Start with a chain of any number. In the 4th chain from the hook, YO (yarn over) and insert your hook into the space. YO again and pull through the stitch, also called pulling up a loop. YO again and pull through the first two loops on the hook, YO and pull through the remaining loops on your hook. The stitch is completed.
Complete the row across, CH 3 and turn. Most patterns I see have this turning CH3 count as your first DC, so you will not be inserting your hook into the last DC you just made from the row below, but into the next stitch.