First, get a new can of shoe polish that is a color that approximates the color of the shoes you want to shine. Old, dried out polish doesn't work too well. Those little Kiwi cans with the clear plastic lid and a foam applicator work great. Then, get a nice shoe shining brush.
Using the brush, knock off all the dust, and if needed, take a damp cloth to wipe off any mud or debris.
Next, using the foam applicator, put some polish on it by kind of grinding it in the polish, kind of like what you'd do to wax a car using the applicator.
Coat your shoes evenly with polish, putting a thin even coat on the shoes, again, like you would if you were waxing a car.
Let it dry for about 5-10 minutes, then put the shoe on your hand and taking the brush, vigorously brush the shoes to a shine.
More coats = better shine.
If you want to learn to spit shine, let me know, the Army taught me well!