I use Sharon Scrambler's method of binding. One of the best quilting things I ever learned. Love the glue basting down. I glue then iron down and wait til next day to finish. Then I wash it.

I also used to press my binding in half before applying it, but since I read on the board about not doing so, and tried it, I am totally devoted to the not pressing. I do finger press the joinings of the binding, or use my wooden stylus, as I go along. I do not use bias binding as I find it both too wasteful of fabric and not better in appearance than the WOF way I cut it. With bias, you are still showing a seam on each side, and mine never seem to be that bulky.
I do stay stitch the edge of my quilt to the backing around the edges before I trim the quilt. It's extra work but helps me keep those edges of all layers together.
I cut my binding just a little wider than most, at 2.75". I do all machine binding and that little bit extra helps me keep the seams neat. I stitch the binding to the back first then fold it to the front and stitch it down. My stitching foot has a little mark just where I need to line it up for nice even stitching on the front.

I will stitch to the front, press it away from the quilt. Then I do glue basting & press the binding down. Usually I can SITD on the front soon after that. I'm stitching 1/8" or less from the binding & catch about the same amount on the back. This gives me the most even binding on the back.

I always press my binding to the outside of whatever side I sew it too. THEN I normally sew to back and flip to the front, glue and press in place, then machine stitch all around in one continuous stitching. My mitered corners are nearly perfect this way. I've used the glue and press to the back for hand sewing the binding too. Works great.
Here's a video of how I do mine.

https://www.youtube.com/watch?v=hsLWzBUTpC0

This is a good example, no matter which side you sew the binding to first.

Well, I did it, I pressed the binding after I sewed it to the front and before I hand sewed it to the back. Wow, it worked fabulously. Have to update my notes on binding a quilt to include this step. Thanks to those who posted information about the technique.