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.
This is my first build ever published, so I may be lacking on some of the latest on Buildcrafting Technology. I'll do my best to improve on the way this looks over time.
As the title suggests, this is my build for a Late-Game Gangplank. It starts Denying, then you'll play a mostly supportive role through the Mid Game until you build your Phantom Dancer / Infinity Edge and start getting Ridiculous and Consistent Crits off Sheen Procs. The itemization suggested is of course something that can and must be modified to suit the opposing team (Like changing Chalice to a Tear of the Goddess / Manamune if there's no need for MRes)
Early Game, you can take Mid if you really have to, but you really want to take a side lane, ideally on the 2v1 if your opponents have a Jungler. Buy a Meki Pendant and a couple HP Pots. Stay by the Nexus and Deny a Melee Creep as soon as they spawn, and walk along with them all the way to your lane. You should arrive just in time to deny a second Creep as they reach the enemy wave. Play defensive using Parley to last hit and keep an eye on your Mana. Deny a Melee Creep every wave, and the Siege Creep every Third. You should get your Ult with well over half a level on your opponent, even if your tower gets roughed up a bit.
Once you get your Sheen, your Parley will start doing some serious damage to opposing squishies. Use your Ult to support your team pushing, to defend lanes, and on Team Fights. Bear in mind your ult is highly RNG-Dependant, so don't rage if one enemy miraculously waltzes through it without taking a hit. You'll get him next time.
If you've already built your Tear or Chalice, mana shouldn't really be a problem, so continue to Raise Morale on every creep wave that happens to walk by. Every little bit helps when it comes to screwing the other team.
By the time you finish Phantom Dancer, you'll be sitting at 57% Crit Chance, and should be able to outrun Kennen's Lightning Rush. When you finish Infinity Edge, you'll be at an insane 80% Crit Chance (Plus 150% Damage from Trinity Procs), and you should have a healthy number of Assists for your teammates. If the game has dragged on this far (And we are assuming it will, since it's a Late-Game Plan) you should be critting upwards of 1.5 K on almost every Parley. If you really must (Or can), get rid of the Mana Item and get a Bloodthirster for added Survivability in the Attrition Wars over the Nexus.
Realistically, you should have starved one lane early enough for your teammates to get the upper hand and win before it comes to selling any items.
I'm not saying this is the ultimate word on Gangplank Wooing Tech. This is just my take on it. Any and all comments are welcome.