A week or so ago I went with Birdman to his Color Guard practice to show the other members how to properly spit-shine their shoes for the upcoming competition. To start, you need the following supplies: Black shoe polish, Navy Blue shoe polish, a piece of an old t-shirt or an old sock, and a pair of old pantyhose.
My preferred shoe polish brand is Kiwi; the little jar of Navy Blue is Meltonian, which is made my the same company. If you can't find it at a shoe repair shop near you, you can order it online here.
Rags and towels made of terrycloth, like a bath towel, are too rough and won't leave a mirror shine on your shoes without a LOT of extra work. In a pinch you can use one of those red shop rags that come in a ginormous box at Wal-Mart. You also need some cold water; not very much.
Finally, you need a pair of shoes to shine. Since I'm not in the military any more, I took my Irish Stepdancing hard shoes on which to demonstrate - it is March, after all, and I might be called upon to dance a jig or two at some point........
Load up your sock or t-shirt scrap with some black polish and start at the toe, working the polish into the leather with little circular motions of your fingers. Keep working at it until you see a bit of shine start to come up. Add more polish if necessary to keep the swirls visible.
When your hand starts to cramp up, take a break and pour a bit of cold water into the lid of your can of black polish. When you come off break, dip the fingers of your wrapped-up hand into the cold water - it will not soak in due to the polish in the cloth, but you'll be able to hold a few beads of water and transfer them to the shoe. Work, work, work this in.
After the first coat with water, get some of the blue polish on your cloth and go after it the same way. Alternate black and blue and water, and after a short while you will start to see the black develop a beautiful DEEP luster and begin to take on a mirror shine. Once this happens, work in one more round of water and take another short break. Next you'll buff the shine up with the pantyhose.
Roll the pantyhose tightly into a sausage; pull out any wrinkles in the material. Hold this firmly in your hand, stick your other hand down in the shoe, and buff like your life depends on it. Alternatively, you can also make a vise with your knees to hold the heel end of the shoe, stretch the pantyhose between your hands, and buff with both hands back and forth very quickly.
Lastly: if your shoes have a line of visible stitching where the leather connects to the sole (the vamp stitchline) you can use an old toothbrush to work polish into this crevice. And if the edges of your soles and heels are faded and scuffed, here's what you need to make them like new. (A black Sharpie marker works in a pinch.)
Admire your work. Use the toes of your shoes as a mirror to comb your hair if you wish!
Allow your shoes to 'cure' for at least 36-48 hours before you wear them so that the polish has time to harden.
When I was doing culinary arts and VIP breakfasts in the Army, I got so I could put such a shine on my shoes that I could wear them for a whole week of shifts in the kitchen without giving them much more than a perfunctory buff-out around the middle of the week.