Not Updated For Current Season
Now that "You Are A Pirate" is stuck in your head, let's talk about Gangplank.
The basic strategy is to stack critical strike chance and critical strike damage, since both your auto-attacks and your main nuke, Parrrley, benefit from them. Once you have lots of crit items, you can start adding attack damage and a touch of lifesteal. In the beginning of the game, conserve your mana by only using Parrrley on enemy champions. Later, once you have more mana available, you can start using it on minions to generate extra gold. You're going to need every piece of eight you can get your hands on, as Gangplank's ideal items are quite expensive. If you need to use Raise Morale, use it on either caster minions or minions with low health. Or both, if the situation arises.
Gangplank was the very first champion I ever played, and even though I was lousy at the game back then (weren't we all?), I had decided to try playing him again, this time with knowledge and experience under my belt. I was not disappointed. If anyone can pull me away from playing Jax for any amount of time, it's Gangplank. Also, like Jax, Gangplank is easy to learn, but difficult to master, but the payoff is worth it. When I was starting out, I was quick to dismiss Gangplank as a novelty champion, unusable for serious play. I will not make that mistake again.
As always, I'm open to comments, feedback, constructive criticism, etc. My summoner name is Dan Highland, and when I'm not using Vandal Jax, you'll most likely see me using Gangplank. See you on the Fields of Justice!