In ArcheAge there are many ways and places to PvP but can be summed up by two(2) basic categories.
Inner Faction PvP
Players of the same faction(also known as Greens) may participate in one versus one battles known as dueling. This is a safe form of PvP as players can not kill each other while dueling.
To request a duel select a player of the same faction, right click their character portrait and select "duel."
Also known as Purpling
It is possible for members of the same faction to attack and kill each other in areas of conflict/war. Murdering the members of your own faction (also known as Greens) by activating the Bloodlust Mode results in the gain of Criminal Points. Players that do crimes like same faction attacking and murdering leave blood traces behind increase their Criminal Points, i
dying with over 50 points will be sent to Prison.
To activate/deactivate this mode, press Ctrl+F.
After activating there is a small delay before it can be turned off.
Cross Faction PvP
It is possible for members of opposing factions to attack and kill each other in any zone that is not currently in a "Peace", "festival" or "Alliance Controlled" state,
Starting zones(under level 30) prevent players from other factions to initiate conflict, but if attacked they may retaliate.
In the deep sea is always war zone and you can become a pirate.