This build will show you how to play Gangplank in one specific way. This way is the way I like to play, so don't assume everyone plays like this. So, into the build, shall we?

*This is only a 3v3 build, so this build should not be a 5v5 build.

This build aims at obtaining critical items as quickly as possible and developing them into more sophisticated weapons.

Pro vs Cons

Pros
Mass damage late game with crits
ulti can hit anywhere (great support)
deny possible
fast movement (late game is like a stabbed rat)


Cons
squishy
requires crit or ap to be useful
hard to farm
low mana
low hp regen
lack of armor

Early Game 1 - 6
I feel that Gangplank is a good Champion for the bottom lane because he goes extraordinary well with other champions. Farm well and try to last hit minions. Also, ALWAYS target the weakest bottom laner and call MIA when possible.

Mid-Game LvL 6 - 11

This is point where you want to be aggressive. There are many ways to do this, as you have your ultimate at level 6. You can ultimate their escape route and run directly into the middle of the AoE. This way, if you are ganking, then you force them run towards you or towards your fellow Champions.

Late Game 12 - 18
Personally, creep in the forest and jungle for the buffs. Be careful as you WILL meet your enemy, so stay close with a pal. Otherwise, use this strategy to attack and initiate.
a) Raise Moral (kill a creep before initiating)
1) Parrrley (w/ Ignite)
2) Ulti/Remove Scurvy
3) Parrrley
4) Remove Scurvy
5) Ghost to escape/chase

People may think this combination is strange and the reason why is that it IS strange. But remember this is for 3v3.

Parrrley is always useful for that extra damage in the beginning, especially because its ranged. The second ability, Raise Moral is perfect early game because it gives you just marginally better stats. The last skill, Remove Scurvy, is always useful as Doran's Blade now costs 475. The reason why I get all three abilities first is for survivability. Remove Scurvy will help for instant HP, Parrrley for harassment, and Raise Moral for deny.

Now that the three abilities have been learned, Parrrley should be the first to be maxed out,and Remove Scurvy when you can. Parrrley will be especially useful with criticals, especially at the point where your critical rating is above 50%. It can do a possible 300+ dmg mid game with possible lifesteal, if you have Executioners Calling.

Remove Scurvy is also an extremely useful ability that will make many enemy Champions rage. Instant HP, great survivability, low MP cost, always a great thing to have before a fight.
Late game, you should always have this ability ready before you engage in team fights.

Raise Moral is the last to be learned because the most useful part of this ability is its increase of movement. Given this build, you will have roughly a 480 move speed. I always found it useful in 5v5s because before a fight, its nice little boost to the team after killing a minion always helps initiate the fight.

Cannon Barrage is ALWAYs handy. Try to be mindful of what your two friends are doing, because they might need it while you are far away. It's also handy for stopping Champions from initiating, chasing, or simply living. Always place the barrage slightly behind the Champions if you are initiating, right above if they are fighting, and slightly towards you if they are chasing. These are also helpful in helping your team mates run away, as it slows the target, whilst doing damage, and it might even turn the tables. :D

Ahhh...Critacular...The steps are now here!
EARLY GAME

1) Begin with Doran's Blade or the Shield, depending on how aggressive you want to be. I tend to buy Doran's Blade because it has lifesteal, albeit small, lifesteal nevertheless. Both items grant 100hp and therefore help a lot during the beginning.

2) Brawler's Gloves/ Avarice Blade/ Boots of Speed
Depending on how much money you have, or who you are laning with, I highly suggest these items. Brawler's Gloves is for the poor, Avarice Blade for the rich, and Boots of Speed for the harrassed. If you have enough money, buy 1 Avarice Blade and Boots. The reason is that you want a good amount of speed, the 12% critical as well as that nice little boost of 1 gold per second.

NOTE: Once you have enough money to buy at least 1 Avarice blade + Boots, go back and buy them. This will give you a serious advantage early game.

3)Avarice Blade/ Berseker's Greaves
Now, these two items are handy because its always nice to have 20% attack speed, 12% critical chance, another gold per 10 seconds as well as increased movement speed. The reason I purchase a second Avarice Blace is simple: cost effective. 750 gold comes very quickly, and the additional 570 for the Besereker's Greaves also comes very quickly. Try to save up enough money to buy both items, you will gain more EXP that way while constructing the build.

EARLY-MIDDLE GAME

4) Vampiric Scepter / Cloak of Agility / Executioner's Calling
These are the next few items. These are to boost your survivability and increase your critacular self. The lifesteal item is necessary for hp, and is your secondary hp regen. The additional 18% critical chance is one of the best things to happen to Gangplank. This should be the item to push your critical chance past 50%. This means that you have a 1/2 change of critical damage. Parrrley is especially good at this point in time, because not only does it help initiate and deal damage in battle, its a great way to finish off your opponent.

MIDDLE GAME

5) Infinity Edge / Phantom Dancer / Youmuu's Ghostblade
Now here is the time where you decide what you want specialize and customize. Here it really becomes situational, so it depends if you want to have more damage, attack speed or finish the Youmuu's Ghostblade.

Infinity Edge - Alway bloody fantastic to have this weapon, more damage, more critical strike, and more kills. Fantastic. The problem is that you have a large inventory already, and its expensive. If you find its too hard to get the gold to finance this, I would highly suggest going the Phantom Dancer route.

Phantom Dancer - I tend to get this one first because its a fantastic addition to the arsenal, giving attack speed, critical damage and a great boost to movement speed. The other reason I get this item out of the three first is because at this point, you will be doing 300dmg crits to opponents, which means, the faster you can move, the faster you can catch up and use Parrrley. Also, Zeal is cheap and easy to get, which is part of the recipe and point of this strategy.

Youmuu's Ghostblade - Now I added this here if you wanted to get it's ability, however I usually get this last, of all items after customization and damage adding things. The reason behind this is because its certainly not cheap. Almost coming in at 2000 gold, getting the Phantom Dancer is certainly more cost effective, but its truly your choice.

LATE GAME

6)Bloodthirster / Frozen Mallet / Infinity Edge
Now, by late game, Gangplank should be critacular. These last items are for certain cases, but at this point, its truly up to you want you want to do with GP. At this point, you can sell your items, go for armor penetration with Last Whisper, Black Clever or what not. However, these are my favourite items.

Bloodthirster - This can both replace your Executioner's Calling, OR, be added for a replacement for hp and never die WHILE killing your opponent. Always good to have that extra bit of damage, plus even more lifesteal. However, the Cons to this, this is a bit unpractical, almost unorthodox. This is just for fun to be honest, but still its an interest build.

Frozen Mallet - This is probably my choice of weapon late game. Slowing the enemy, extra life, more damage, definitely a great weapon. If you get to the point and have a good tank, you are set.

Infinity Edge - Stacking? Never heard of it. Simply put, more damage, more critical chance, what more do you want?

Masteries
Gangplank is an offensive Champion in this setup. Utilities should be optimized to enhance GP's EXP gain and his Ghost movement, for both chasing and escaping.

The offensive masteries are optimized for maximum critical chance. The reason why I have critical chance rather than critical damage is because having more critical damage ensures you have an almost consistent high level of damage. It's bloody brilliant when GP crits with Parrrley.

Summon Spells: Ignite / Ghost, Exhaust / Ghost, Ignite / Flash.

Ignite/Ghost - This is my combination. Ignite for 50% less hp regeneration and 150 dmg, good early game and great against Champions like Mundo.

Exhaust/Ghost - I sometimes use this in the case that another Champion that has that ability and I feel like rather than damaging my opponent with ignite, I want to slow him. This will be the case if you don't have a stunner, slower, flashing champ etc.

I feel that Ghost can be replaced with flash if you so desire.

Well, this is my build, please feel free to comment, but if you do dislike or vote down, please comment and explain why.

If you do vote up, please add any additions you want me to add. Otherwise, please try it!

02/13/11 UPDATE: Changed the masteries, and item build, on recommendation from Jet.