Hello everyone,
here is my guide about one of the strongest AD Carries (even with all those nerfs) there is in the game. I try to give you an idea how you carry your team to the win and how you play effective in farming, ganks, teamfights etc.
So here we go...

Pros:

- range
- great laning abilities
- great escape ability
- one of the strongest lategame AD carries

Cons:

- squishy
- highly farm dependent
- hard time against melees without range
- highly teamfight dependent

I go for a 21/0/9 Masteriestree. In the offensive tree I dont use Lethality , because Corki is not a Crit dependent AD Carry just like Ashe etc. I spend two of these points in Alacrity to make it up to 4 and the last one in Offensive Mastery .

I prefered to use the last 9 points in the Defensive tree because Strength of Spirit is just one of the best masteries for staying longer in the lane. The other 6 points go to Hardiness for better for armor and the other 3 for Resistance to be able to be stronger in 1v1 fights early game against the opponent carry.

Hextech Shrapnel Shells: It is just an awesome passive for an AD DPS Carry like Corki. Opponent tanks got a really hard time against this passive because their is no Item which saves them from true damage. One of the reasons why Corki is one of the best AD Carries out there.

Phosphorus Bomb: The spell you will mostly use in the laning stage or later on in quick pushing/defending of the lane. Since the nerf it is not that much usefull anymore in lategame and teamfights. But you can harras/gank really good with it early on.

Valkyrie: A Flash with 8 seconds Cooldown. Great for initiating, escaping through walls or getting some range between you and the opponent Champion(s).

Gatling Gun: Great for fights, and early agression in fighting the carry in 1v1 situations. If you use it for laning and farming early on, you will push the lane to hard and find yourself fighting at the enemy tower. So dont push with it!

Missile Barrage: This is another Spell great for laning/pushing/defending, because of its low Manacost and 1.2 seconds cooldown. It is great for outzone the opponent carry, defending your turret from save range and farming like a mad man. Just another reason why Corki is what he is.. an incredible carry!

Greater Mark of Attack Damage : Better then Greater Mark of Desolation for Corki because it helps your passive Hextech Shrapnel Shells.

Greater Seal of Attack Speed: Is really good in fights 1v1 against the other AD-Carry.

Greater Glyph of Scaling Mana Regeneration: For some better laning ability and to spam your Missile Barrage even more without running out of Mana.

Greater Quintessence of Desolation: Stacks with your Hextech Shrapnel Shells as well and gives you some more harras and lasthitting power!

Early game:

Pick up a Doran's Blade at the start and as you farmed a bit just pick up a couple Boots and another 1-2 Doran's Blade for some lasthit and laning ability.

Core Item:

Just try to farm up as fast as possible and then get Berserker's Greaves and Sheen what should give you already a lot of power. Try to farm a Trinity Force in at least 25 minutes to be really powerfull. Now you are ready to be an important part in teamfights.

Late game:

But to keep on being an effecitve carry for your team, try to get as much free and save farm as possible. Your next item can be Bloodthirster if you are farmed up well and got some kills, or a Banshee's Veil if you struggle with AP Champions. This is the point, where you have to make your own decision!
Also Madreds Bloodrazor and Last Whisper are great damage items for Corki to shoot down heavy lategame tanks like Cho'Gath.

Exhaust: Great to escape together with Valkyrie or to get take an enemy of with Valkyrie.

Flash: Best summoner spell out there, nuff said!

Farm, farm, farm and.. FARM for FAME! This is what Corki is about!
In best case you get a supporter on your lane like Sona who dont take lasthits and heals you like crazy if you are harrased.

Try to harras your opponents with Phosphorus Bomb and as you hit level 6, spam your Missile Barrage as much as you can on your opponent to outzone them, get them on low hp and then from your lane by killing or letting them portal.

DONT AUTOHIT! I know some players just autoattack all the way just like "I get my gold this way as well". But this way, you push the lane forward so dont do that. Just lasthit low hp creeps to get your farm up. range creeps need 2 Corki hits and 1 tower hit, while melee creeps need 2 tower hits and 1 Corki hit.. KEEP that in mind!
You may use your Phosphorus Bomb to get 3 lasthits at ones or something like that, but dont waste your mana to much for farming!

If you dont got a supporter on your lane or even play on a solo lane just try to play defensive, and farm up as good as possible. Let your lanepartner do the initiation and then just go in with Valkyrie, shoot your Phosphorus Bomb and activate your Gatling Gun (if needed, use Exhaust for a sure kill). If the opponent espcapes barely, you might get him with one or two well placed Missile Barrage.

Corki is a highly team dependent carry, but if you are in the right position you will make a ton of damage to your opponents. Just make sure you outrange the opponent heroes and make sure that you dont get be focused or you die really fast. To get in a new and right position is fairly easy with Valkyrie and Flash, which can be used really well for that.

Dont be the first who goes in the teamfight! Just shoot from a save range with your Gatling Gun and Missile Barage. Dont use your Valkyrie to go close in the fight, if you are not totaly sure, that you wont be nuked down. Corki dies really easy to opponent AP carries like Malzahar.

OK guys,
that were my first guide and I hope you liked it and know now, what ever you wanted to know about Corki and the reason to come here. I might work some more things out at this guide in the future, just let me know what you liked and disliked ;)

Were you able to carry your team?!