One of the main features of Destiny is the player vs player combat. You can’t just jump in like most games and if you don’t know where to look you might miss it. Find out where you need to go and how to unlock PvP in Destiny here!
The Crucible is the PvP area of Destiny. You will need to complete The Last Array mission on earth before you can access The Crucible. After you complete that mission head to orbit and to the right of earth you can see the PvP area. You use your character and gear in this mode against other players. The game tries to get you a 6v6 if possible but it will go with less players if it cannot find 12.
Before you start PvP you should go grab the bounty quests from the bounty board in The Tower. Here you can find PvP specific objectives like win X amount of matches or kill X amount of players with a head shot. Once you get high enough rank with The Crucible you can buy new weapons or Sparrows from the quartermaster downstairs. Each of them costs a certain amount of Crucible marks but they are high powered weapons. The weapon levels are 20 but if you can afford a Sparrow it doesn’t matter what level you are. If you want all the gear expect to grind for a bit.
Now that you know how to PvP I expect to see you in the Crucible ASAP!