To make the screen:
I treated this just like stretching a canvas:
Lay your fabric on a flat surface and put your frame over it. Fold up one edge around the frame and in the center, staple it to the frame. Now pull the material from the opposite side, make sure it is taut, and put a staple in to secure it. Now, repeat this in the other direction. You should have four staple in the center of each frame-bar. You can now work your way adding staples outward as you pull the material taut and toward the corners. It doesn’t have to be perfect, just tight enough that its not floppy and doesn’t stretch too much.
If i didn’t have this staple gun I might have success with a regular office stapler if the frame’s wood is soft enough, or maybe strong tape that will stick and hold to the fabric and frame.
I also lucked out and had a nearly ideal fabric to use as screen mesh. It’s from an old curtain or curtain-liner and is see through and synthetic, which means it will dry fast and not shrink/stretch. I also have some gauze-y cotton, sort of like a cheesecloth, that I am trying, just to compare. This one will take longer to dry, might stretch a bit when washing, but I think it should still do the trick.