First, make sure to have decent bourbon in the house. Cheap stuff is too raw, and you probably don't want to use Booker's for this. Maker's Mark answers nicely, or Woodford Reserve if you're feeling particularly flush. On no account use any ersatz bourbon from Tennessee.
Traditionalists to the manner born use silver cups. Among us plebs, a good squat glass with a solid bottom will do nicely.
Harvest mint, rinse it, and pat it dry with paper towels. Put about a teaspoon of sugar in a glass and mix it with just enough water to dissolve it. Add a few mint leaves and muddle them thoroughly. If your equipment lacks a muddler, the handle of a crab mallet will suffice.
The ice is important. It should be cracked ice. Crushed ice will melt too quickly, producing a weak and watery julep. Whole ice cubes will not produce the correct balance. So take some cubes, put them in a plastic bag, wrap it in a kitchen towel, and wale away at them with a rolling pin.
Fill the glass with cracked ice and pour bourbon over it until the ice is covered. Garnish with a mint leaf. Sip. Reflect that life is good and give thanks to the Baptist clergy for their two great contributions to Western civilization: the separation of church and state, and bourbon whiskey.
Then, when the band plays "My Old Kentucky Home," shut your mouth and stand respectfully.
Then you can watch horses run around a track, if you like.