I starch my fabric *before* cutting into squares. Starching stabilizes the fabric so it doesn't stretch when you are cutting it. This would be especially helpful when you are cutting scraps with varying grainline directions.
For me, the absolute most accurate way to sew HSTs has been to use Thangles. Here is a link to them on Keepsake Quilting:
http://www.keepsakequilting.com/productdetail/8787.htm
I tried the template cutting method illustrated elsewhere in this thread also but found it to be too time-consuming for me. Plus, I tend to start gritting my teeth when precise cutting is required.
Thangles require removing the paper afterwards, but I found that to be a nice task for tv watching and didn't mind it. I've only used Thangles with strips of fabric, but you could easily cut the paper strips into squares and use them on scraps. I probably wouldn't even cut the scraps until after they were sewn together with the Thangle. When cutting the paper down the diagonal, I would probably just use the paper guide to trim the edges at that time.