Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
~~~It won't let me show it, but buy Avarice Blade (1-2) early when buying your Zeals (get 2 of these asap) but sell them later, with 2 Avaraice, the mastery, and Parrley last hitting you can farm up more gold than anyone.
This is the build I do when I play Gangplank, it's not that strong early but is a beast mid/late game once you get a few items farmed up and max out your Parrley/Morale.
Start the game with Meki and 2 health pots, harass with Parrley and last hit like a beast, you want to stay in lane until you reach 2715 gold, or if you get a couple kills in lane, try to stay until you hit 3465. This lets you pick up Manamune (covers every single mana issue you gives good AD that just grows over time), Zeal, and Avarice off the bat. I don't use boots on Gangplank because with Zeal/Phantom Dancer and his Raise Morale you are very fast already, and it gives you more gold to spend on AD/Crit, and gets you your Infinity Edge that much faster. Your core items are Manamune, Infinity Edge, and Phantom Dancer x2, after that I usually tack on Bloodthirsters for the big damage boost and lifesteal, or can build defenses with Banshee's, Guardian Angel, etc.
Remember to always use your ult, as often as you can when the opportunity arises. It can clear a huge group of minions from the other side of the map, including those at the turret, leaving a champion forced to run and saving a turret... it is also amazing for team fights, adding some damage to everyone but more importantly it's an AoE slow. Always aim for where the enemy will be running too, never drop it just on top of someone - cut off their escape and crit their face with Parrley!
Raise Morale is an amazing skill and makes you a great asset to the team, not only does it make you very quick and adds damage to you, it does this for your entire team when you have a minion to kill, letting you run, chase, kill a turret in seconds, anything that a boost in speed/damage would help. It also has a fun bonus that if you are with TF, everytime you use it you get the 2g from killing something even though it's your own minion :P
Get one rank in Scurvy at lvl2, and save it for when you get CC'd. Late game if you pick up Golem you can spam it to heal, but it's main use is for the CC removal and it does just as well at rank 1 than at rank 5, the only difference is shorter cooldown and bigger heal. Due to not picking up boots with this build, Raise Morale is more important (and more damage/group help) so just max this last.
I have had much success with this build, over about 100 games I've gone about an average of 10/5/15 which I think is pretty good for solo queue 5v5, if your tank is good you can wreck face... it's very hard to catch Gangplank that has 420+ movement speed, Flash, Ghost, and Scurvy... don't let the enemy kill you!