Step 1: What You Need
The first thing you'll need is one of those telescopic mirrors that mechanics use. You can get one at most hardware stores or any auto supply store. I started out with the small sized mirror which worked just fine, but this time I got the jumbo size to "upgrade".
You'll also need 2 or 3 alligaror clips. The reason I say 2 or 3 is this: you'll need 2 alligator clips and one "just clip". I used a small portable reading light that I got at the $1 store. This way I always have a handy light. If you don't want to bother you can use another alligator clip (for that matter, for this part you can use a clothes pin.)
Now for attaching everything, you can use either solder, or like I did, Epoxy weld, or JB Weld. (I stink at soldering). Some zip ties might also prove handy.
For tools, all you really need are a pair of pliers. I made the one pictured with nothing but a multi-tool.
Step 2: Getting Started
Also, remove the "handle" covering from the mirror. Mine just slipped off, but you may have to cut yours off.
Now there's no rule saying you need all of the tubes in the telescopic part of your mirror. In fact, if you have a broken one lieing around, you can save yourself a few dollars. I would recomend you keep at least 2 though so you can adjust it easily. Mine only had 2, so I didn't have too many choices.
By holding the mirror against your hat (on your head, of course). You'll get an idea of where you'll need the clips. Mark those sopts on the tubes with a sharpie.
The Epoxy weld says that it hold better if you rough up the area. I used the file on my multi-tool to make some scratches.
Step 3: Attaching the Clips
Next, following the directions for your weld, mix it up and slather it on the flattened ends of your alligator clips. Then lay them flat onto the area you marked earlier. Remember, there's no reason you can't remove the mirror temporarily to make everything lie flatter. Also, keep a piece of plastic under your work space. I used a piece of zip lock bag, so when it glued to the bad, I just cut the bag up.