GrendelsBane

World of Warcraft has a few different PVP options available to those not on a PVP server. You can challenge someone to a Duel. Form an Arena team team. Or join a Battleground.

Dueling is pretty obvious. You challenge another player to a duel then fight one on one till someone wins.

Arena PVP is an ongoing tournament, available in 2v2, 3v3 and 5v5 formats.

There are four existing Battlegrounds: Warsong Gulch, Arathi Basin, Alterac Valley, and Eye of the Storm, with a fifth planned for Wrath of the Litch King. Each Battleground has a different format, accepts a different number of players and has different level requirements. You can enter a BG from the Battleground Masters in each capitol city. Each BG has a holiday weekend. These weekends begin on Friday morning and end Tuesday morning. During the BGs holiday weekend you gain increased honor and reputation. You can find the official schedule on the Events Calendar on the World of Warcraft website. Each time you complete a BG you receive Marks of Honor (1 if you loose, 3 if you win) and Honor Points.

Battleground Daily Quest:

Patch 2.3.0 introduced new daily BG quests. The quest givers can be found in any capital city near the Battleground Masters. The quest objective is to win a specific battleground. They give honor, gold and XP; the reward varies by level (11G 99S and 419 Honor points at level 70). Only one daily is available per day and is randomly chosen from the list. Available daily quest varies between servers. — WoWWiki

Players can use Honor Points with Battleground Marks of Honor to purchase items in Stormwind’s Champions’ Hall or Orgrimmar’s Hall of Legends. You can purchase armor, weapons, trinkets, potions, gems and even mounts.

Points to remember: Killing another player whose level shows up in gray gives no honor. Typing /bg when entering a Battleground allows you to join the Battleground chat. Using Shift-M will bring up a small zone map in the lower right hand corner of your screen. This map will help you keep track of where all your team members are.

PVP can be pretty fun. Just remember you earn more honor by winning than farming kills.