This is my no-binding method for finishing a quilt.
Sometimes binding is fine and necessary, like for a lap or bed quilt, or for a contest that has specific rules, and a binding can add additional visual interest to an art quilt, like here:
But sometimes you don't want that. Sometimes there isn't one particular fabric that will enhance the piece. I prefer this look for my art quilts.
There are several methods for facing a quilt. This is how I do it. It's the easiest, I think.
Square it up.
Cut your facing strips. I always use black or a dark color because it doesn't show. Width does not matter, as you will see. These are pretty wide, as I was cutting into a 12" piece, so I cut four lengths of 3" each, but they can be any width. Fold one side under, press, and stitch down.
This is how the facing strips will go. Notice the bottom strip is not long enough to cover the entire side of the quilt--no worry. I could have patched it with the extra from the other side, but it's not necessary.
Sew the strips to the front of the quilt, right sides together. I have no idea how big my seam allowance is, nor do I care. Fold the strips to the back and press them into place. You can see the gap where the strip was short. Doesn't matter.
It doesn't matter because you are going to fold the long piece over the gap.
Voila. Perfect, crisp, 90 degree corner. No hassles. No cutting 45° angles, no turning and poking. You just need to whip-stitch the facing to the back of the quilt and you're done.