There are two PvP dueling arenas in Dark Souls II, one for the Blue Sentinels covenant and one for the Brotherhood of Blood covenant.
The Blue Sentinels dueling arena is located in Heide's Tower of Flame after killing the Old Dragonslayer (Ornstein). Join the Blue Sentinels and you can pray at the statues near the bonfire below to start a duel. To join the Blue Sentinels initially, and to start each duel, you need a Token of Fidelity. You earn Tokens of Fidelity by using your White Sign Soapstone, and after being summoned, helping the summoner defeat the area boss.
The Brotherhood of Blood dueling arena is found in the Undead Purgatory after killing the Executioner's Chariot. Talk to Titchy Gren and join the Brotherhood of Blood, then pray at a statue for no cost to duel (so much better than the Blue Sentinels). To reach the arena from Majula, head down towards Heide's Tower of Flame, but have Licia move the path. (If she isn't there, you need to talk to her more after the Dragonrider boss fight, also in Heide's Tower of Flame).
Each Brotherhood of Blood win earns you a Cracked Red Eye Orb. Each Blue Sentinels win gives you a Cracked Blue Eye Orb (at the cost of a Token of Fidelity). You can buy both Cracked Orbs in New Game Plus for 10,000 souls.