Fold the 2-inch binding strip in half widthwise and press it.

Begin in the center of one side on the back, rather than at a corner. 

Line up the folded raw edges of the binding with the edge of the quilt, leaving three or four inches of binding fabric extra. Stitch the binding to the quilt along this edge with less than a 1/4-inch seam allowance. Stop about 3/8-inch before the corner.

At the corner, fold the binding fabric up so that it makes a 45-degree angle at the corner.  Then fold the fabric back down so that its' raw edge is aligned with the second edge of the quilt. It helps to pin each side of the 45-degree angle closely to keep it in place.  

Sew a seam along the second edge, beginning at the pin so that you don't sew the angle.  Stop approximately 3/8-inch before the second corner, and repeat folding.  This prepares a neat mitered edge on the front of the quilt.

Once you have sewn around three sides and returned to the first side, it is time to stitch the ends of the binding together.  Unfold both ends and lay them open on the quilt with their edges aligned with the edge of the quilt.  In this photo, the edge I began with is on the right.  It lays on top. 

Using the beginning edge as a guide, mark the 45-degree angle where it lays on the other end of the strip.  With a clear ruler, draw a second diagonal line about 1/2-inch beyond the 45-degree mark.  This will be your seam allowance.  Trim the bottom strip to this line and sew a 1/2-inch seam, right sides together.  Press the seam open to make it less bulky; snip off excess points.  If you need to, repress the fold of the binding strip.

Sew this edge as you did the first three sides.  

Now you can turn the quilt over and begin to sew the binding over the edge of the quilt.  I always like this part!  It helps to pin the binding in place along the edge you are working on, or you could use binding clips.

The tidiest stitch for sewing a finished edge is Blindstitch. Hide your knot by beginning at the raw edge of the quilt that will be covered by the binding.  Come up from the bottom and snag one or two threads from binding fabric, just beneath the fold.  Return to the bottom fabric, as close to 1/8-inch away from your first stitch as you can.  This can be tough at first, but it only takes a few stitches to get the hang of it.