Here is a quick photo recap of my favorite way to make HST (half-square triangles). Somehow, early on in my quilting life, I ended up with the nifty little tool seen below:
I bought mine ages ago, but I found it online here recently.
So you position your two squares right sides together and make three lines down one diagonal as seen above.
Next, aligning the left side of your foot with the dotted (or center line), sew two seams on the two solid lines. In this way, you could chain piece a bunch and then come back down the other side.
Finally, slice with your rotary cutter through the center line and, voila! Two HSTs!!