It is abbreviated to "hdc" in crochet patterns.
1. Yarn over the hook.
2. Insert the hook into the next stitch.
3. Yarn over.
4. Pull the yarn through the loops. Now you have 3 loops on the hook.
5. Yarn over again. Pull the yarn through all 3 loops on the crochet hook.
6. Half double crochet stitch is finished.