This stitch starts like a double, but ends like a single. So assuming you have mastered the single crochet (SC) here is what you do to master the half. Just before inserting your hook into the stitch, YO (yarn over). Then insert your hook, (YO) again, pull through the space, or sometimes I say pull up a loop, YO and pull through all remaining loops on your hook. There should be three.
Tips about turning the HDC: Usually you chain two and turn and HDC into the very first HDC of the row below. The chain two usually does not act as a HDC like a CH 3 does for DC. I’ve seen patterns that only have you CH 1 and turn as well. If you are simply practicing and want to create a swatch, stick with the chain 2.