This can be earned quite early as a barbarian, by about level 7/8.
On the skill tree second section, Core Skills, select Upheaval -> Enhanced Upheaval ->Violent Upheaval.
With that as long as your skill hits at least 2 enemies you will begin Berserking for 2 seconds. Simply use it on a group of enemies and you'll light up in flames for a few seconds to show you are Berserking.
Edit:
Also as mentioned by andrews1022 if you select your basic skill as Lunging Strike -> Enhanced Lunging Strike -> Combat Lunging Strike you can potentially start working at this even earlier/have more chances to berserk, though it only activates on a critical strike so it may not be as effective.