Welcome to my first guide, for Gangplank.
This build will focus on Crit Gangplank, which is IMO fun to play, very fun to play.

PROS:
Fun to play
Easy Harrassment
CLEANSE and HEAL in-build
AoE Ulti so AoE damage and slow
Insane damage with Parrrley

CONS
Quite squishy
Doesn't deal tons of damage with ulti
Not great at escaping

For Runes I take:
Greater Mark of Desolation - Armor Penetration, you need this to ensure maximum damage, combined with Youmuu's Ghostblade you will have enough Armor Penetration.

Greater Seal of Evasion - Dodge, always nice to have, but these are quite expensive, with Greater Seal of Scaling Mana Regeneration (which are cheap), you won't encounter Mana problems, even though I don't think Gangplank has those, so Greater Seal of Armor will give you armor to block some minion aggro, because you want to harrass a lot, for a very cheap price.

Greater Glyph of Scaling Cooldown Reduction - Cooldown Reduction, also very nice to have, to trade Ionian Boots of Lucidity for better boots.

Greater Quintessence of Critical Chance - Crit Chance, early game boost, with Masteries and Brawler's Gloves you will Crit a lot with your early game harrasment.
If you don't like these, there are always other quintessences like
Greater quintessence of desolation for more Armor Penetration

For masteries I build a standard DPS 21/0/9 build, grabbing Improved Exhaust and Neutral Buff Duration.

Starting Items:
Brawler's Gloves and Health Potion
Great crit chance combined with Runes and Masteries, early game harrassment (make sure you don't spam too much, because you can run out of mana).
Potions are self-explanatory.

When going back:
Avarice Blade, Boots, Sight Ward
More crit chance and gold, later building it into a Youmuu's. Boots are self-explanatory.
You NEED wards to avoid ganks, always buy a ward or 2 if you have some extra gold to spend.

Then go for:
Brawler's Gloves, Mercury's Treads, Sapphire Crystal -> Sheen
Crit chance, building it into Executioner's Calling, Improved boots for speed and Tenacity and Magic Res, if you think you don't need this, buy Berserker's Greaves for an attack speed boost. Build the mana crystal into a Sheen for more damage output

After that:
Executioner's Calling
Lifesteal, Critical Chance, and a poison, with Grog Soaked Blade and the Lizard Buff you deal tons of damage with Parrrley, adding 3 DoT on-hit effects which also slows (lizard and grog).

Then:
Infinity Edge
Insane Damage output, start with the B. F. Sword because you don't have any extra damage items yet.

After that:
Phantom Dancer - Youmuu's Ghostblade
Crit chance, Move+attack speed, great item for GP.
Then upgrade your previously bought Avarice Blade into Youmuu's Ghostblade and activate it when you need it.

Final Items:
Trinity Force - Elixers
-You can always buy elixers though, these will help you a lot that 4 minutes, make sure to buy Elixir of Agility and Elixir of Fortitude, Elixir of Brilliance won't help that much unless you really need CDR.
Trinity Force will give you basically everything, plus an improved effect from Sheen, even chance to slow more!

If you want, sell you Executioner's Calling to buy Bloodthirster for more lifesteal and damage, instead of 15% crit chance, it's your choice.


Other nice items
If the enemy team has AP champions, you need magic res:
Banshee's Veil
For more survivability/durability.
Quicksilver Sash
To remove ALL debuffs including the full Exhaust and Ignite or even Children of the Grave and Hemoplague
If the enemy team has AD champions, you need armor:
Atma's Impaler
Is nice because you have armor, AND crit chance, plus a little damage boost with it's passive.
Warden's Mail
Is also nice because the slow is just awesome, upgrade it into Randuin's Omen if you want to be tanky, with a nice active as well.

However, a Frozen Mallet with that massive health will make you a little bit tanky as well, also the passive is awesome.

PASSIVE: Grog Soaked Blade
Gangplank's attacks deal damage over time and apply a slow that stacks up to 3 times, last 3 seconds.
This is an amazing passive, it's annoying as hell for your enemies.

Parrrley
Gangplank shoots an enemy unit with his pistol, dealing damage and gaining extra gold if the unit is killed.
This is your main ability that you are going to use, this can deal insane damage, and it also applies on-hit effects!

Remove Scurvy
Gangplank eats some oranges and it'll be okay, healing him and removes CC effects.
This is your cleanse, and your heal, this can removes Stuns, Snares, Fears, Taunts and all that other ****ty stuff. It can even removes the Exhaust's slow (but the other effects will still be there).

Raise Morale
Passively gives Gangplank a flat amount of damage and movespeed, when activated, Ganplank shoots in the air, giving him and nearby allies bonus damage and movespeed.
Good for chasing and damage output, also, get yourself an assist by shooting into the air while your teammate does the job.

Cannon Barrage
Gangplank targets an area on the map, cannonballs will hit that area, dealing damage and slowing all enemies in that area.
AoE damage, use it in teamfights, use it to slow people, use it to killsteal/get an assist, a great ulti even though you need to be lucky and it doesn't deal tons of damage.

Maxing Parrrley first will give you the best harrassment.
At lvl 2, need health? Get a point in Remove Scurvy and a point in Raise Morale at 4, if not, the other way around.

Once you have Parrrley maxed try to balance your abilities, and ofcourse take Cannon Barrage when you can.

For Summoner Spells I take:
Exhaust to slow an escaping enemy, or one that's chasing me, also applying the bonus effect from Cripple.
And
Flash for chasing or escaping.

Other good summoner spells:
Ignite to ensure champion kills. (Alternative for Exhaust
Ghost to chase or escape. (Alternative for Flash
Teleport to control the map. (Alternative for Exhaust
Smite when jungling. (Alternative for Exhaust

When jungling, grab Flash and Smite.

Start with a Vampiric Scepter and take out the wolf camp with Parrrley
Smite the big wraith and learn Raise Morale.
Kill the golems and recall, get a Cloth Armor.
Head to the Blue Golem and kill it with your abilities, using Smite when it's around 500 health.
After this clear the jungle, get a Wriggle's Lantern and the rest are basically in the guide, finally sell Wriggle's for Bloodthirster or an Executioner's Calling.

That was all I wanted to say about GP, please leave a comment below and I hope you enjoyed reading this.
Thanks for reading, -DrunkAsianFather