According to WoWWiki and several other websites, Justice Points are rewards for participating in normal and heroic dungeons that match the character level.
I've been doing random dungeons using dungeon finder since lv15. I am now lv65 and have been in 20+ instance runs, but didn't receive a single Justice Point, nor did I find any place on the game interface that mentions anything about them.
Did I miss something obvious?
Best Answer
Due to its volatile nature, any answer posted about Justice Points is likely to change quickly (at the very least with every expansion, sometimes with a patch).
A good place to look is Wowhead. It's officially supported by Blizzard and is considered the WoW bible by many.
Here is a list of ways to obtain JP (and ways to consume them as well): Justice Points
There are just way too many to list and the formating will probably drive me mad. I will just list a few ways you will get them once you hit Pandaria.
From patch 5.0 or maybe an earlier patch, you have to be level 70+ to start earning Justice Points.
You can check the amount of points you have by opening up your character page, and clicking on the currency tab.