found old quilt blocks
 

Can anyone tell me how to finish the block?

I think I would applique it on a coordinating background.

Applique sounds right. Maybe on denim to make a pillow?

I've seen similar blocks put together with neutral or white squares and triangles inset between the diamonds. These require "Y Seams", which may be why the units were never finished. Is the fabric thin and loosely woven? Might be a detrimental factor to working with them, unless you really love them or they hold sentimental value.

Here is a diagram of the block known as "8-Pointed Star"

I would applique it onto a square of fabric and probably make a dresser scarf or table topper out of it.

Here is a blog tutorial that you could skim through to the part about setting into the background. http://hopefulhomemaker.com/2013/04/...lock-tutorial/

I think I would put a piece of muslin on top, sew around, leaving an opening, then birth it. Press well and machine applique or hand if you want onto the background of your choice. that would give some of those fragile edges some support and cover the seams at the same time. (can you tell I would not want to deal with Y seams?!)

I have 8 blocks. I found a box of old blocks for $3 at a thrift store. They are not the best quality but interesting.

I was thinking of doing that. i have 8 blocks.