For skyshards and fishing, you can mostly stay off the radar. Prepare for random deaths, but mostly you'll be by yourself.

To unlock the PVP skills, you'll have to actually PVP. Easiest way is probably to slot healing springs with a resto staff, go towards the swords on the map, and heal your allies.

Ah, non vet zone seems like it would be the right place for me then thank you ^^

Get your mount speed and stamina to max asap. Cyrodiil is a big place. You'll depend on your mount when the map is controlled by other alliances and you have an objective deep in their territory. Do the PVP training, should be enough to unlock Rapid Manuevers, and slot it. All this will help when you need to return to delve or fishing hole after you get ganked on the far side of Cyrodiil.

Expect to be ganked. Your only options are defend yourself or stealth and hope to get lucky.

Earning AP is not hard. Nilmot has a good suggestion. Or you can repair walls, defend keeps and resources, or join a group (safety in numbers).

I never planned on playing PvP as well. I went in just for The sky shards. And actually got most of them with very few deaths. Sometimes I had to do some hiding out for a few minutes. Then one day I stopped at keep under siege and man! The first time was enough to suck me in! It is so much fun! People attacking the wall, siege equipment on the walls firing back. Fighting on the ground, and then rush when the wall goes down!! Doing PVP is a blast! But some nights the lag and constant game crashes can get annoying.

Try to group with a buddy. It's actually very enjoyable with a couple good friends. For the most part, people in delves won't attack you from another alliance. They are likely doing the same thing, wait a moment to see their intention first.

For PvP skills. Buy wall repair kits and fire ballistas. Support type skills like Restoration staff mutagen will rack up AP at a fair pace.

4 Skyshards can be tricky to get. 2 inside each of the enemy alliance gates. They'll be the first two Skyshards listed for each Alliance Zone. Rapid maneuvers (Speed boost) and decent horse stamina helps a lot to get through the gate. There will be NPC mages and the like spamming powers at you on your way through.

My advice to you would be: "SNEAK"

Once you get to PvP, start sneaking. Sneak everywhere you go. If you run out of stam then stop, and sneak again. As you are sneaking around Cyrodil. Repeat these words of a warrior as you sneak: I am such a noob, I am such a noob,I am such a noob.

Hope that helps, and welcome to Cyrodil

Try to get Rapid Maneuver skill asap. It helps a lot and you will love it even outside of pvp zones.

As disintegr8 said, be prepared to die a lot. Be prepared to deal with lag and the consequences.
Use food to boost your health, magicka, stamina.
Carry tri-pot healing potions and/or immovability potions which prevent you from being knocked on your a** by certain skills.
Poisons are handy
Use stealth when you can
AP comes from capturing resources, keeps, towns, repairing walls, doors, siege & killing other players.
Be prepared to be ganked while roaming around the map trying to get skyshards.
You also gain skill points each time you level up through the alliance war ranks.
There are a lot of guides out there for builds in regard to pvp. Or you can run with whatever you choose.

Get impen gear. Sometimes it'll be just enough to get away from a ganker instead of dying. Then you don't have to cross the entire map again.

Also, don't be afraid to actually try to pvp, it really is very fun. You'll die much more than you'll kill someone but it's a good way to learn. Everyone else's advice is spot on, just make sure to have fun.

Yes, get impenetrable trait gear, especially if you are a healer. I made some for my healer on the weekend and could not believe the difference it made to my ability to survive, even with 5 pieces of light armour.

Get your alchemy and provisioning up to max rank or at least put skill point into passive for duration on both crafting. As far as I can see nobody gave mentioned that you can use invisible pot even if don't have NB.

Don't forget that you also can buff your allied in different ways, so there is more way to help out then by spamming heals.

As Supportive skill you have Purge (AW skill line) which is very important to combine with healing spring or other heals as siege weapon often have poison or fire DoT which can kill you fast as you will have more then one DoTs during a fight around places where siege weapon is being used.

Stamina on mount help you to ride longer with full speed upgraded and to be able to ride past NPC before they can force you off your mount.

Don't forget to look at your map for where a fight is going on (crossed sword) and where you can travel, if you would be killed. Map is a very important tool in PvP as "safe zones" where you alliances had keep and resources can change very fast while you are occupied with PvE like skyshards and doing quests. Scout mission is virtually just travell to place confirm that have been there (press button to make a report) and then go back for your reward which will give you AP. You will also get AP from completing quests, that way you will get ressorces (AP) which you can use to buy siege weapon and repair gear for walls. Don't repair siege weapon as those have such short time when nobody is using them to degrade and be gone.