You will be opening this thing a lot. Find fasteners that take minimal effort to operate. I chose the snap buckle you see, which unfortunately was the only one left in the store (why I have only one strap instead of two).
Alternatives are velcro, snaps, or the shoelace tie of the true traditionalist.
Go slow and use a sharp needle on webbing, of course. But other than that, it is just throwing a few good rows of stitches in, and pulling it through the hardware of your choice. (For a really traditional look, recycle an old belt or spend some time distressing raw leather strips from Tandy -- see my other Instructable.)
Oh, right. And there's the edge treatment, which I didn't get any pictures of.
Practically anything will do to finish the edge. Double-turned seams (if you use curved edges like I did, these can be quite a hassle of clipping and folding, though). Bias tape, or self-bias with one of the fabrics you've used, or a contrasting fabric.
Or decorative edging like this; I found some faux leather stuff that stretched easily and was fairly simple to bend around the turns. I held it in place largely with small binder clips (you can't really pin it), but it is a bit of a pain to get it lined up properly so that your stitch falls that clean 1/8" from the edge on both inside and outside. In a number of places, I failed, and I even ripped out a few feet, but at first glance it doesn't look too bad.
And it protects the edge from fraying, and looks cool while doing it, which is what it is for. What, really, about half of what you will ever do with fabric is for.