A half-closed ring is simply that--a ring that has only been closed halfway.
Begin the HCR the same as you begin a ring. Tat all the stitches according to your pattern's directions. When you close the ring, stop when the ring is halfway closed. It will look something like this:
If you have HCRs in a pattern that parallel each other, be sure to measure the one you're closing against another that is already closed. That way you will get them all closed the same amount.