There are many different ways to attach binding.
Here is a YouTube video that does a good job of explaining how to machine sew a relatively invisible binding (especially if you use invisible thread, but that's a subject for another post!). The creator of the video hand sews bindings only for quilts that will be in a show.
http://www.youtube.com/watch?v=wprg5vzkuGw
Oops! Sorry, didn't see the second page of posts until mine came up.
That is a beautiful quilt!
Mary