Here's how to make a half-double crochet:

1. Begin with a foundation chain, leaving enough chains for your desired stitch count. For this example, let's create a foundation chain of 20 chains.

2. Yarn over. This means you'll wrap the yarn around your hook from back to front.

3. Insert your hook into the designated stitch (the stitch you want to work into). If you're working into the 4th chain from your hook (as is common for the first row of half-double crochets), insert your hook into that chain.

4. Yarn over again and pull up a loop through the stitch. You should have three loops on your hook.

5. Yarn over one more time and pull through all three loops on your hook.

   You've successfully completed a half-double crochet. Continue these steps for each stitch across the row.