Sure, the modern system is simple enough, but if you want to be really l33t, you have to know the traditional system as well.

Before the Meiji Restoration, the Japanese day had twelve hours, which were assigned to the twelve signs of the Chinese zodiac. Where Europe used bells to mark the hours, Japan used taiko drums. So you had:

  • 11 PM - 1 AM: Hour of the Rat (ne) 9 drums
  • 1 AM - 3 AM: Hour of the Cow (ushi) 8 drums
  • 3 AM - 5 AM: Hour of the Tiger (tora) 7 drums
  • 5 AM - 7 AM: Hour of the Rabbit (u) 6 drums
  • 7 AM - 9 AM: Hour of the Dragon (tatsu) 5 drums
  • 9 AM - 11 AM: Hour of the Snake (mi) 4 drums
  • 11 AM - 1 PM: Hour of the Horse (uma) 9 drums
  • 1 PM - 3 PM: Hour of the Sheep (hitsuji) 8 drums
  • 3 PM - 5 PM: Hour of the Monkey (saru) 7 drums
  • 5 PM - 7 PM: Hour of the Chicken (tori) 6 drums
  • 7 PM - 9 PM: Hour of the Dog (inu) 5 drums
  • 9 PM - 11 PM: Hour of the Boar (i) 4 drums
Each hour was subdivided into four quarters (hitotsu, futatsu, mitsu, yotsu) with which you could express times down to the half hour. One expression from the period was Kusaki mo neru ushi mitsu no toki: "The third Hour of the Cow, when even the trees and grass sleep..." That would be 2-2:30 AM by our clock.

Yes, it's quite vague, but it was good enough for a pre-industrial society, and they did scrap it after they started to modernize.