If I'm going to use the binding right away, I do iron it in half and, as I go along, I let it fall into an empty waste basket. Then I sew it right to whatever side of the quilt I want. Lately, I've been sewing it to the back and then machine sewing it to the front.
If I'm not going to use it right away, I iron it in half and just wind it over my hand and store it in a baggie that I attach to the quilt top. Then when I finally sew it to the quilt, I take it out of the baggie and let it puddle onto the floor as I sew it on.