Gangplank is a very fearsome pirate indeed, especially after the buff he got in the recent patch. The most notable buff he got was to his Grog Soaked Blade. Stacking it to 5 to get the most out of it requires getting up close and personal, however, and many guides build Gangplank way too squishy to do that safely. The goal with this build is therefore to make him tanky enough to be able to take some punishment without folding like wet paper and still packing enough of a punch to be able to 2/3-shot squishies when fed.

The most important skill you will need to pull this off with any kind of consistency is good last-hitting, especially with Parrrley. If you are good at this you should always be a monster all game, every game.

Let's begin! YARRRRRRRRRRR!!!

ArPen marks and quints, health/lvl seals and flat CDR glyphs are my runes of choice. If you want you can replace the marks with %crit ones, but since not many champs benefit from such runes compared to ArPen it's more convenient to just run ArPen. For seals and glyphs, you could use flat or scaling armor and magic resistance if you prefer. Flat will give you a significant advantage in the early laning phase and scaling ones will make you a bit more tanky late-game.

Greater Mark of DesolationGreater Mark of Desolation
Greater Seal of VitalityGreater Seal of Vitality
Greater Glyph of Focus
Greater Quintessence of DesolationGreater Quintessence of Desolation

Other choices:

Greater Mark of Malice
Greater Seal of Resilience
Greater Glyph of Warding

23/6/1, a strange setup it may seem at first, but when you look at it it actually makes sense. The defensive masteries make you a bit more durable, especially in the beginning. 23 points in offense lets you pick up all the bits you need, most notably 10% crit dmg, 6 ArPen and 4% increased damage. The point in ghost would of course be moved if you use some other summoner spell.

Start with Meki Pendant and two Health Potions for that crucial mana regeneration that lets you use Parrrley almost anytime you want. Then buy boots and rush your Infinity Edge. If you farmed well with Parrrley you will have it early and the surprise damage when you crit will give you many kills. After that buy a Cloak of Agility that you will later build into an Atma's Impaler, but hold off on doing that until you have built a Frozen Mallet. It will give you a hefty slow on your Parrrley that will allow you to get in melee range and apply more slow with your Grog Soaked Blade. Now build your Atma's Impaler, it will give you a good amount of crit, armour and damage aswell since you have the hp from Frozen Mallet. Now that you have armour you need magic resist - Banshee's Veil. An added bonus is that the health from Banshee's Veil also gives you more damage since you have Atma's Impaler. If you are facing a team rich in magic users you will need to buy Banshee's earlier. By now the game should be over but if it isn't you should finish the build off with Phantom Dancer.

The skill sequence is pretty straight forward. Max Parrrley first, take a single point in Remove Scurvy and max Raise Morale second, taking Cannon Barrage whenever you can. If you are getting harassed hard you might want to consider taking one or two more points in Remove Scurvy for the additional heal.

I prefer to use Ghost/ Exhaust, but any of the following are viable:
Ghost
Flash
Ignite
Exhaust

Red Buff: Gangplank is probably one of the champions that can make the most out of the red buff, at least until he gets Frozen Mallet, at which point it gets a bit redundant.

Making good use of Cannon Barrage: Gangplank's Cannon Barrage can be used for escaping, chasing, helping out teammates, saving towers and killing escapees. In short, it is extremely versatily and useful. Good map awareness is crucial for every champion, but even more so for those with global ults. So always keep an eye on the minimap if you want to make the most out of Gangplank.