This is part of my post on binding problems. There is more in Posts #33 and #35. Those posts also expain how to join the ends of the binding in a mitered seam that looks like all the other seams in the binding.
I don't take the quilt out of the machine when I get to the corner. I sew up to a seam-width from the corner (if your binding will be 3/8" wide, stop at 3/8" from the corner. Turn quilt 45 degrees away from you and sew right into the corner, but keep the needle in the last stitch. You may have to back up one stitch to keep the needle still in fabric. Turn the quilt so that it is in position to sew down the next side. Lift folded edge of binding and pull loose binding down toward you. You've just created a big wrinkle in the binding. Pinch this wrinkle and lay it flat to the left. You've just created the perfect folded corner. If you need to, lift the needle now, but don't move the quilt too far away from the needle area. Be sure the fold in the binding is even with the last side, and edges of binding and quilt are even along the next side. Give binding a little tug so that it lies flat. Move the quilt so that the needle is at the next seam line. You will have one seam width of loose thread there. Just leave it, don't cut it off. Start sewing down the next side, no need to back-stitch.
Happy quilting