This makes it just a little easier if you press your triangle before you start sewing on the binding.
Jenny Doan has a very good lesson on finishing bindings in all of her Block magazines. The only thing I would add to that would be to start with the "Magic Triangle". (I iron mine first!)
When your beginning of the binding is laying on the quilt in the right place, open the strip and fold the top left corner down so that this top edge is even with the right side of the binding strip. Fold the binding in half again. Press very well. Put a pin at the "sweet spot", the spot at the base of the triangle, where the triangle meets the edge of the binging strip. , and start sewing about 6 inches from that tip.
When you have sewn on most of the binding, stretching the binding at least a little as you sew it on, and come around to the end, stop sewing at least 6 inches from the tip of the triangle. Take the quilt out of the machine. Pin the beginning tail to the quilt where you will want it to be, keeping it very snug. Stretch just a little. Then pin the ending tail where you want it, stretching that a little, too. Cut off ending tail at the sweet spot. There is a pin there, remember? When ending tail is cut off, take out all pins.
Now use a binder clip or Clover clip to hold the quilt edges together where there is no binding yet. This just makes it easier to work without all that weight in your way. Open both binding tails out flat. Place right sides together matching top edges. Find the diagonal line you pressed in. Twist the binding edges so that that diagonal line is horizontal and tails are at right angles to each other. Pin well. Sew on pressed line. Press seam open, you should see a square in there with a diagonal line through it. Trim the seam allowance. Fold in half again being sure the seam remains open. Sew this last area of binding to the quilt.