Hi and welcome to Corki, The Ace of Bandle City.
In this build i mainly focus in attack damage but with a bit of ability power to full your abilities. The main focus item is
Trinity Force and Bloodthirster

I start with the Greater Mark of Magic Penetration to get armor penetration.

Greater Quintessence of Attack Damage and Greater Glyph of Attack Damage are to get more attack damage and have a more strong beginning.

Greater Seal of Replenishment are to get some extra mana, cause when i am with Corki, with this build, i still use my abilities a lot and to have mana to keep using gives me some advantage.

In my masteries, i go 21 in Offense because Corki is an AD Carry and you should want to get the most damage from your basic attacks.

Then i put the 9 points in Defense for durability and health regen.

Pros:
+ High single target burst damage
+ AOE damage
+ Shreds armor
+ physical, magical and true damage
+ Excellent farmer
+ strong poke and harass
+ strong early-mid game nuker
+ Amazing late game dps
+ Built in flash-like ability
+ Urfrider skin is epic

Cons:
- Mana dependent
- Auto attack range is 550
- Lacks any form of CC.
- Low base movement speed
- Somewhat hard to play and master

Hextech Shrapnel Shells
Corki's basic attacks deal 10% additional true damage to minions, monsters, and champions.


Phosphorus Bomb
Corki fires a flash bomb at a target location. This attack reveals non-stealthed units around the blast and champions for 6 seconds.
Deals 80/130/180/230/280 (+0.5) magic damage to enemies in a target area. In addition, the blast reveals the area and champions hit by the blast for 6 seconds (does not reveal stealth).


Valkyrie
Corki surges to target location, dealing 60/90/120/150/180 (+0.4) magic damage per second to enemies in the fire left along his path.


Gatling Gun
Corki's gatling gun fires at all targets in front of him for 4 seconds, dealing 20/32/44/56/68 (+ ) physical damage and reducing 2/4/6/8/10 armor per second. The armor reduction stacks and lasts 2 seconds.


Missile Barrage
Corki fires a missile toward his targeted location that will collide with the first enemy it hits. Each missile deals 120/190/260 (+) (+0.3) area magic damage.

Corki stores one missile every   seconds up to 7 missiles at any given time.

Every 4th missile will be a Big One, dealing 50% extra damage.


Hextech Shrapnel Shells
Corki's basic attacks deal 10% additional true damage to minions, monsters, and champions.

To start, i get a Doran's Blade and aim right away for Berserker's Greaves. My next item is one of the main aspects of this build, the Trinity Force. It just gives Corki a really good advanatge, since it gives so many great buffs to you. Next, another very important aspect is Bloodthirster, that gives you lifesteal and damage, and thoose 2, help you a lot when using Corki. My next item is Black Cleaver for damage and some attack speed so that you can make your enemies fall out of health faster. Instead of Black Cleaver you can get a Youmuu's Ghostblade or Last Whisper. Then i keep the damage going finishing the damage with a Infinity Edge. My final item is a Banshee's Veil for some health and mana, and also in the case you going against an AP champion with a lot of stuns, it gives you some advantage.

Situational items

• Madred's Bloodrazor if the enemy team as a tank
• Thormail if the enemy team as a feed AD
• Guardian Angel if the enemy team has very little CC or none
• Quicksilver Sash if the enemy team as a lot of CC Cleanse, take this as a replacement, instead of the Banshee's Veil that only blocks one CC every 45 seconds.

I believe Flash and Exhaust work very well with Corki, since the Exhaust let's you finish off the enemy champions faster and the Flash let's you get close to them easier and also helps if you need to escape.

You can also use Ignite instead of Exhaust if you prefer to be able to finish off your enemies in case they use flash and you can't get to them.

Ghost is also a good choice if you think that your Nocturne needs speed instead of being able to jump away of tight places quickly. Ghost also let's you get to your enemies faster or if your enemies are pushing or you need to help a teammate,
Ghost may let you get to him faster or get to the turrent where they are pushing faster.

I hope this build help you get a great score with your AD Carry Corki,The Ace of Bandle City.
Say what i need to improve, vote and comment.