The main purpose of AP Gangplank is to get a lot of damage from your ultimate. Having a large damage output from your ult will allow you to apply pressure to other lanes without ever even leaving yours. With a little map awareness you can pick up several assists and kills.

Aside from increased damage on your ultimate, your W will also heal you for an insane amount once you start getting some AP.

The first item that is rushed on AP Gangplank is Sheen. This item will grant you increased Q damage, as well as CDR and mana. This solves most of your early game problems.

The next item that should be picked up is Fiendish Codex. This item provides a little bit of AP as well as 10% CDR.

After Fiendish Codex has been acquired, it is best to go ahead and rush Lich Bane, perhaps buying Boots of Speed somewhere in-between if your budget allows it. Lich Bane interacts with your Q, allowing it to deal magic damage based on your AP. This adds some usefulness to your Q, and it also provides AP and CDR which are very necessary for Gangplank to get the most out of his ultimate.

The next complete item that should be obtained is Nashor's Tooth. This item is purchased for its CDR, AP, and passive. Its unique passive allows your basic attacks (Gangplank's Q) to deal 15% AP as magic damage. This works well with Lich Bane to increase your Q's damage. The attack speed it gives is also nice, although not as important, which is why stinger is not built before Lich Bane is already completed.

Another essential item that will be needed is Boots of Lucidity. This will cap your CDR, enabling you to get the most uses out of your ultimate.

The final core item that should be picked up is Rabadon's Death Cap. This item gives the most AP, so it is perfect for increasing your damage.

Items to top off your build include those such as Luden's (for extra ult damage), Liandry's Torment (to combat teams with a little bit of MR), and Void Staff (to combat teams that have a lot of MR).

Taking Assassin may seem a little odd, but since you won't be leaving lane a whole lot as AP Gangplank, you won't be around your team very often. This means that your ultimate will benefit from the increased damage provided by this mastery, no matter where on the map you target.

Bandit is a nice mastery for Gangplank, because you actually gain 10g from using your Q against an enemy champion rather than 3. Even though your Q is a ranged basic attack, you are a melee champion so you get the 10g. Combined with starting Spellthief's, you can gain a lot of gold simply from harassing your lane opponent.

Intelligence is taken so that you can go past the CDR cap, meaning you will achieve 45% CDR before the game is over.

Thunderlord's is also really nice on Gangplank because his ultimate can proc it. I have tried Deathfire Touch as well, but I find that Thunderlord's is a lot better since it provides your ultimate with nice burst.

-Early laning phase should be all about farming with your Q so that you can begin gaining Silver Serpents which are used to upgrade your ultimate
-Try to harass the enemy laner with your Q when you know you won't be missing any minions for it
-Always try to reserve at least 100 mana once you reach level 6 so that you have the ability to use your ult
-Only use your W for sustain when you know you won't be needing it any time soon to get out of CC
-Ult placement is everything on AP Gangplank. Always be checking the map for opportunities to kill an opponent, or to assist a teammate when they are in a fight
-The first wave of your ult with Death's Daughter deals extra damage in the center of the ult, so try to center it on a squishy target
-Barrels can be used to gain vision of bushes so you aren't required to face check them. They can also be used to slow your enemies
-Placing a barrel under your turret is a good idea if you feel like the enemy might try to dive you