Note that while specific materials are mentioned here, substitutes are readily applicable. For example, using Coat hanger wire instead of galvanized wire as well as using duct tape in instead of epoxy/SuperGlue. You don't even need to use the rectangular mirror. You can use the circular type or make a rectangular mirror from a circular one. in all cases, a convex mirror is most appropriate. Flat mirrors just don't have the coverage of a rectangular convex mirror.
Step 1: What you need
1. Special Mirror (see image and description below). Typically found at auto parts stores like AutoZone
2. About a foot of 14 gauge galvanized wire (or similar substitute like copper wire). I find aluminum and copper wire is not stiff enough. It seems to always get bent out of shape. Galvanized wire holds its' position very well. Wire from a coat hanger would probably work just as well!
3. An alligator clip (or other suitable substitute). Alligator clips with teeth work the best but they will mar a surface. Other "toothless" clips seem to always slip out of alignment.
4. Epoxy (or other suitable adhesive). Five minute epoxy seems to work best as it provides a bit of time to assure correct placement as well as provide a large adhesion area. Superglue tends to pop loose when twisted.
5. About a 3 inch by 2inch bit of strong self adhesive tape.
You'll note that other than the specialty mirror, everything else can be found around the house. The mirror itself can be cut out of a circular mirror. Why rectangular? Well it allows for a wider, single glance horizontal view of what's behind you while eliminating a lot of vertical view that is not needed in a circular mirror.