Player Vs Player combat is another way to enjoy ESO but it can be intimidating for new players. I hope that you find the resources here help you to try this aspect of the game.
Alliance Points are used to level the Alliance War Skill lines. These skill are helpful to all players, both of PvP and PvE. Skills all players should unlock are Warhorn and Vigor (for Stamina-based players).
AP is gained through killing other Players in PvP enabled areas, taking objectives in Cyrodiil and Imperial City and doing quests in Cyrodiil.
The fastest way to earn AP is to participate in battlegrounds. Even loosing them will get you a substantial amount of AP. However, you should still enter Cyrodiil at L10 and do the introductory quest and get 2 free skill points.
THE THREE ALLIANCES
When players create a character they're asked to pick one of the three Alliances - Ebonheart Pact, Aldmeri Dominion, Daggerfall Covenant. Your character's alliance has little impact on the overall game except for in Cyrodiil and Imperial City.
In these two areas you may only group with those of your own alliance, and you can only kill those of the other alliances. You cannot change the Alliance of your character, but you can make a new character in another Alliance.
All my characters are in the Ebonheart Pact alliance. ^_^
PVP ENABLED AREAS
Cyrodiil is the overland PvP area. Reach it by opening your Alliance War menu (L by default on keyboard) after you reach L10and setting a Home campaign. Campaigns are 30 day CP-enabled, 7 day CP-enabled, 30 day CP-disabled and 30 day under L50.
Combat in Cyrodiil involves taking objectives such as defended keeps by knocking down the walls and stacking on the flags at the centre until it flips to your alliance. It's very satisfying!
If you are top of the campaign leader-board and your alliance holds all of the central "ring" keeps you become Emperor (and loose it again as soon as one of the keeps is lost again).
I have a series of videos that can help you get familiar with Cyrodiil and I often take groups of Twitch viewers into PvP and teach them what to do.
Imperial City is a mix of PvP and PvE areas. As of the Elsweyr Chapter, there will be one CP-enabled campaign and one CP-disabled campaign.
There are Bosses both above ground and below in the Imperial City sewers. Fighting these is made more challenging as there is always the risk that another player might happen along and decide to jump in. At the centre of the sewer you can fight the replica of Molag Bal for valuable extra rewards.
Fighting in IC earns you the Tel Var currency which can be used to buy IC specific armour sets, as well as rare materials. When you die in IC you loose half the Tel Var you're carrying, and if it's a player who killed you - they get the Tel Var.
Battlegrounds are 15 min or 500 point limited (which ever is reached first) 4v4v4 matches. Battleground types include Deathmatch, Crazy King, Murderball, Capture the Flag and others.
Unlike Cyrodiil or IC, they are not locked to alliance so you can group with anyone. Queue for either over or under L50 Battlegrounds via the Group Finder (all Battlegrounds have CP disabled).
Battlegrounds have associated leaderboards that you can compete in, 1st and 2nd place battleground rewards including exclusive motif pages.