Cover: In AoP you got 2 types of cover, full cover and partial cover. The full one obscures the vision. The partial one makes you less likely to get hit by enemy. Don't try to fight enemy on open space, unless your team clearly outguns the enemy at a long distance. Always stay somewhere near full cover. In addition to that, you can also create your own cover from snipers by throwing smoke grenade between the point you want to cover and a sniper. The smoke can be used for defense against sniper, for offense against sniper lane and for defensive offense if you want to deploy your machine gun/minigun and shot blindly at enemy without being targeted by snipers.
Information: It is important to have info about the enemy before you engage them. If you can, poke behind cover to check for enemy positions. There is specific tactic to aid your team, quickly press space to enter RTS mode, then use right mouse clicks to quickly ping enemy locations. This should be performed under 1 or 2 seconds, in the meantime your character should have been ordered to move behind the cover.
Weapon ranges: You need to be aware at least of the basic weapon ranges, you don't need to know specific number, but more less how far it reaches. For instance, DSR outranges m1c, however simply thinking like that will get you killed. You need to deploy DSR, this wastes action point, you dont need to deploy m1c. M1c can easily take down DSR by closing the distance by moving between covers.
Support your allies: This isn't just about first aid or to defibrilate them, they are minor things in teamplay, but even minor things can save the day, although rarely, that's why they are minor. The most important way to support your teammates is to shot when they shot, expose yourself when they are exposed. If the enemy splits his damage between 2 players instead of 1, then your chances of survival will be higher. Unless enemy uses machine gun, but that's what for is the advice "Information" for.
Know your weapon: You need to be familiar with the upsides and downsides of your weapon. This isn't as simple as you may think. An example ? Steyr is a weapon for 42 hex range combat, a middle distance, the AK-74 is better most of the times, but it has 34 distance range, that's close distance. Pancor is 22 hex distance weapon but it easily outdamages AK-74. If i am to pick a weapon that gives both damage and range, it would by Steyr. So what's the lesson ? It takes around 4 seconds to kill with Pancor, it takes around 8 seconds to kill with Desert Eagle .50, yet Deagle outddamages Pancor in most cases. How is this even a math ? There is 2v2 fight, exchange of fire through windows, one side has a sniper and machine gun and deals average damage, the other one has 2 gattlings, each dealing very high damage. Yet the gattlings lose, how come ? Figuring out answers to those questions requires game experience with different weapons, so go ahead and seek most deadly combinations, but remember that "deadly" doesn't apply to all situations.
Voice chat: Do not underestimate this. It's much faster to say few words than to write them. Joining the voice chat should be done as preparations for PvP, not during PvP and not after the fight to play and coordinate even better by using voice chat next time. Even listening to others without speaking yourself gives you an edge.
Determination: You lose the fight and you and your team will take shit gear and go for funzies next fight and maybe you will win, you have nothing to lose. Sure that's fun in it's own way, but no way to win the fight. You need take it more seriously, to make tactical analysis of what you did wrong, of the enemy arsenal, of the possible places where it can be rendered less effective, then come back better prepared. If that doesn't work, do it again. This way, you will become better players much faster than if you did things for funzies.
Tactical positioning: This task usually falls upon the leader/collective to pick a spot where you will fight. Do not pick places where you will be overwhelmed from multiples sides easily. Pick places with cover, in big fights, places where reinforcements can arrive easily.
Hold your squad dear: The PvP is not over because your team loses once, you don't die in reality from that. However you can lose your teammates if you keep blaming everyone constantly, or being a bully to others. This is a social skill, something that allows you to win fights by outnumbering your enemy and is visible only in long terms, not during single fight. Be a person worthy of the respect, not a person hated by everyone. Everyone gets angry from time to time and says things he regrets, it's important to say sorry for those bad things you've said.
Know when to retreat: You need to be aware of when to pull back from fight and reorganize the team. This also includes the times when the fight goes on for too long and your team is running out of supplies. Or when you've lost too many people and enemy didn't. Do NOT run in panic, else enemy will hunt you down and you will miss the chance when enemy leaves himself open for swift and effective counter attack if they pursue you and break formations. It's better to save what's left of you than to lose everything for no reason.
Crowd control: It is vital for your team to have some kind of crowd control weaponry, like fire grenades, like miniguns, machine guns, door glue, anything that can stop the advance or rush of the concentrated enemy forces.
Know the mods: There are mods like noroof, noreload, attack-move, open-enter doors. They were created for a reason, it was to speed up things you do in pvp. You should master them and use them. They have downsides too, but provide you with advantage over others who do not use them for stubborn reasons. It's like not using super stimpacks or drugs simply because you don't like it, even if it could have saved you.
Be on guard: Just because you don't see the enemy doesn't mean there is no sneaker around you, waiting for the chance to take you down. The only safe place is your own room/base and world map. Not even HQ courtyards are safe from fire grenades.
Secondary weapon: The secondary weapon of choice is and never should be your primary damage dealing weapon. This is something you should take for situations like those: A 2v2 fight is about to take place, me with pancor and my buddy with sniper are fighting against 2 snipers. What would be the problem then ? The problem would be me with pancor and the inability to support my ally and attack the enemy that is 60 hexes away. This is where high level players have advantage over low level players (low level = above 24 but below 39), because high level players can have more than one weapon skill at 250% or 225%, thus allowing them to pick secondary weapon from bigger arsenal. Remember, the secondary weapon needs to complement your primary weapon. Like this (Primary/Secondary) Shotgun(green)/Steyr, Shotgun(white)/ACOG, Shotgun(white)Laser rifle, Sniper rifle/H&K shotgun(White), Sniper rifle/Grenade Pistol, Melee/Steyr, Melee/Grenade Pistol, DSR/M249, Gattling/Super sledge, Minigun/Rad rifle, Avenger/Rad rifle(in inventory, not equiped), Pistol/Grenades there are many many more combinations, i just wrote but few of them.