(Not the whole cutting, machine sewing part, just the hand stitching bit)
I've been told I do nice bindings. I guess if you have to find *something* nice to say about my quilts... ;o) I've also noticed on several of the quilting forums that I visit, new quilters understand how to do the initial part, but are stumped when it comes to the hand sewing step. I see time and again people recommend a hem stitch, or a whip stitch, and suggest that seeing the stitches is just part of the deal. It doesn't have to be.
I don't use a hem or whip stitch to sew bindings down; I use the same stitch that I use for hand applique, the Ladder Stitch. It disappears like magic, especially when using fine silk thread for applique. For bindings I use doubled cotton thread, whatever's handy and matches the backing more or less. Since it really does disappear, I'm not so concerned about the colour.
Step One. Knot the end of your thread and bury it in the to-be-bound quilt edge and batting. Bring the needle out just below the line of stitching that attached your binding to the front. Make sure you do not run the needle through the front of the quilt. Check. Often.
Step Two. Fold the binding over the edge, covering the attachment stitching. Insert the needle directly (vertically) above where it emerged from the quilt body and take a small "bite" of binding, right through the inside. Pull the thread through loosely.
Step Three. Repeat that small "bite" in the quilt body, inserting the needle directly (vertically) below where the needle emerged from the binding. Pull the thread through loosely. You will see your stitches. Don't worry about only grabbing backing, or always grabbing a bit of batt. This isn't about rules, it's about magic. ;o)
Step Four. Repeat the small bite stitching, alternating binding and body for five or six (or 8 or 9 or 10) stitches. Don't fuss about the number, just don't wait too long.
Step Five. Pull the thread tight to make the stitches disappear. Magic.