The Badge of Justice currency was introduced into The Burning Crusade as a way for players to obtain raid quality gear outside of raids, giving more meaning to farming heroic dungeons in the early game.
In a later phase, Badges of Justice will also begin to drop off raid encounters making them much more obtainable and farmable.
For the current phase, however, they are only obtainable from boss drops in heroic dungeons and completing a daily quest that sends you to retrieve an item from one of these dungeons.
WoW Classic TBC: Badge Of Justice Guide
The most effective way of farming Badges of Justice is to simply run as many heroic dungeons as you can.
Each boss is guaranteed to drop one badge on kill, however, heroic dungeons can only be completed once per day, so you are limited on how many you can earn in a day, although there are currently 15 different dungeons in the game, and it is unrealistic to complete all of them in a day.
Players from both the Horde and Alliance can visit Wind Trader Zhareem who can be found in the Lower City of Shattrath.
Each day he will task players to venture into one of the heroic dungeons and complete a specific task for him, and he will reward players with 2 extra Badges of Justice.
This can be a good quest to complete daily as it can add quite a bit of extra badges on top of the dungeon you complete, especially if you do not have much time to play.
G'eras can be found inside the Terrace of Light on the second layer and will sell players items for 25 - 50 Badges depending on the item.
More vendors and quests will become available in a later phase, however, Blizzard has yet to announce the full plans of the five phases
The new quests and vendors are tied to the daily quests in Isle of Quel'danas, which players may expect to see released along with the Sunwell Raid in phase 5, although we could maybe see the dailies released in a 4.5 patch.