For your black mirror, you will need:
1) A relatively dry and warm day
2) A pane of glass (I myself have only ever done this with glass; perspex/plexiglass might work as well, as it has a very similar reflectivity, but is much more easily scratched); I got mine from a cheap Wal-Mart picture frame.
3) A piece of backing (felt, cardboard, etc) the exact size of the glass
4) The glossiest black paint you can find (semi-gloss is right out). I have had success using spray-on lacquer but glossy automotive paint is supposed to be ideal.
5) Window cleaner and either paper towels or newspaper
6) A sheet of white paper at least as large as your piece of glass.
Step 1: Prepare Your Materials
Before getting started, you'll want to clean the mirror on both sides extremely well. I find a glass clear and newspaper works the best, but microfibre cloths also work.
Once the glass is clean, set it on top of the white piece of paper (without smudging it); I used two 11x17 (ledger) sized pieces of paper to make sure I didn't accidentally spray my sidewalk. If you only have a piece of white paper about the size of the mirror, use newspaper or a dropcloth.
You'll also want to shake the spray can according to the manufacturer's instructions; for my lacquer, this took about a minute.
Step 2: Paint
Once the first coat is down, let it set for a few minutes before spraying another layer. You should be able to see the white paper through the glass if it isn't totally covered, as in the picture (from my first coat). In the case of my lacquer, subsequent coats covered the glass fully but seemed quite rough: this didn't make any difference to the final mirror, as far as I can tell, but your mileage may vary.
When all the coats are down, follow your manufacturer's instructions for letting it dry; mine said that it would be dry enough to handle an hour later.
Step 3: Backing
If you use a plain sheet of glass, you'll want to glue some cardboard or felt to the back to make sure the reflective backing doesn't flake off (as you sometimes see in old mirrors). Normal PVA (Elmer's glue) should be fine for this: It's flexible, long-lasting, and dries slowly enough that you can rearrange the backing piece before it dries if need be.
Step 4: All Done!
Enjoy your new mirror!