I want this to become a Corki blog which I will update frequently to make sure you guys are up to date on how to dominate with him. I would like to hear some suggestions on how to improve my layout to make it more reader friendly because the information it provides should be easy to take in.

Welcome to a guide about my new favorite champion: Corki The Daring Bombardier. I have found great success with this build because it offers superb farming capabilities paired with insane damage as well as a lot of ways to keep the enemies from killing you. If played right it is hard to get a negative score with Corki, I really can't imagine why the poor guy has no more than 11 builds on this site.
I actually find Corki the best ranged carry in the game and most top players would say the same thing. Reginald's tier list puts him in the top early game carry and Elementz' tier list puts him right below pantheon as the second strongest solo qeue champion.
This is a very similar build to the one that was used in a recent high yield tournament by the winning team's Corki(both teams had Corki) and also very similar to the way HotshotGG builds him.

Table of contents:

Pros and cons
Match History
Pregame
Game and item walkthrough
Some information about why this build rocks

Pros and cons

Quite frankly there are many pros and few cons to Corki, especially with this build.

Pros

Crazy burst damage
Very strong sustained damage
Good escapability and some survivability
Insane creep farmer
Fun to play
Great champ to carry a team even if they are bad
Shreds tanks apart
Strong laner
Long range poke/finisher
Good chaser

Cons

Squishy (though you shouldn't be in a position where you can get focused)
requires a bit of practice
You have to know your limits to be succesful
You have to focus a lot on farming until you have Trinity Force

My match history

These 10 games were played right after I got him, before these I had only played 3-5 games with him. The games were level 30 normal games. I will upload some recent match histories soon. I died more than necessary in these games because I was testing his limits and making reckless moves here and there as well as getting used to Corki.

Pregame

Runes

Greater mark of Desolation
Armor pen, Best runes to increase damage and that's what carries are all about.
Greater Seal of Scaling Mana Regeneration
Mana regen/lvl, These help me out so much with harassing and farming.
Greater Glyph of Cooldown Reduction
Cooldown reduction, You arent getting any items with this so it's nice to have 9% from runes and masteries.
Greater quintessence of Desolation
More armor pen, so even more of that sweet dmg.

Masteries

I go with the standard 21/0/9 ranged carry build. 21 in offense for damage and 9 in utility mainly for the exp. The 5% is actually very good.

Skill sequence

Max out Phospherous Bomb first, picking a level in Valkyrie at level 4 for the escape/chase capability. 2nd skill to max is gatling gun and ultimate when available.

Summoner Spells

I have been loving the Flash/ Ghost combo for a while now, 2 escapes that can also be used offensively. As a carry you will get focused so you need to be able to escape, early on flash may help you to get first blood by landing that last auto attack on the enemy or surprising him with a Q>E>auto attack combo. The same goes for ghost, It can also be used to get to fights faster if your jungler is getting ganked for example. Corki has an escape spell of his own but trust me, you will need more than that if you want to stay alive against good players.
I understand that some people might not like these choices so I will provide some alternatives.
Teleport
Good summoner, can be used to gank, get to your lane in no time or backdoor/defend a tower.
Exhaust
Also a good summoner spell, can help in ganks and teamfights and also be used both defensively and offensively just like flash but I just think flash is superior.
Ignite
pure offensive spell, wouldn't really pick this but it might help you finish some kills or shut down that mundo.
Cleanse
Not a bad spell at all, just not as good as flash or ghost.

Other spells would be highly ineffective for Corki, don't bother with those.

Item and game walkthrough

Starting out

I always take mid with corki, he needs some farm and can solo very well, you might even get first blood but we're not aiming to play recklessly. Instead we aim to farm up a storm by last hitting well and later use a Q+R combo to kill a wave of caster minions and just spam R on anything that can give you money if it dies. If you aren't hindering your jungle you can kill the wraiths with 1 combo of Q+R for some extra farm.
Corki is powerful at harassing so against some enemies you can play agressively and try to get a kill, however do not take risks because dying is not worth it.
If you don't go mid this guide would still work but you would need to farm a little longer, making you less powerful compared to the others.

Doran's Blade Health Potion
Cookie cutter starting items that do the job very well.

Boots
Pick up boots first time back unless you have money to buy Tear of the Goddess

Tear of the Goddess
Great item for Corki if you turn it into Manamune. If you get it early you can stack it up. It will also enable you to spam your spells to farm and harass.

Mercury's Treads OR Berserker's Greaves
It's time to make your choice about which boots you will need most. If the enemy team has some nasty CC Mercury Treads are a must. If not, Berserker's Greaves are the best alternative.

Enemies that require Mercury's Treads

Veigar: His cage is very dangerous, at high levels it stuns quite for quite a long duration, paired with the range it's terrible for Corki.
Amumu: 2 stuns, bad for Corki.
Ashe: you never know when that Ashe arrow from across the map will hit you, she also slows with each attack and mercury treads make your escape that much easier.
Fiddlesticks: Fear level 5 lasts for centuries, without Mercury Treads a good Fiddle will be your downfall.
Rammus: Don't even get me started on his taunt...
Even against teams without these CC *****s Mercury treads can be the better option. If they have multiple stuns/snares or very high magic damage you might want to pick them up.

Midgame

By now it's midgame, you may have to stay at tower if your opponents are missing, only leaving it to quickly kill all the minions for gold with your abilities. Your main priority is still to farm until you get your hands on Trinity Force, though if an oppurtunity arises you could gank or help out your teammates with dragon.
I see a lot of players that just run around from lane to lane trying to get a kill when they are around level 10 but this has no real use and will only make you fall behind in exp and gold. You have to manage your time effectively to become strong for when the real teamfighting starts. Don't stand around with 3 people on a lane after a failed gank, either the gank worked and you try to take tower or you go back to farm. Also tell people that hang around mid lane taking your exp and gold to go back to their own lane.

Neutral Buffs

With this build you really do not need golem buff and you should leave it for someone who does.
Lizard buff is extremely powerful for Corki, when you are level 8 or higher you can easily kill the lizard by using your abilities and you should get it whenever it's up unless you have a jungler who needs it to gank. When you have lizard you can play more aggressively and be confident in a 1 on 1 fight. It's also amazing for ganks.

Ward POWAA

Another thing to note during midgame is that it drastically increases your chances of succeeding if you buy a ward once in a while. When you are at the base and you have bought another of your key items and are left with some gold, pick up a ward! You could use it to make sure nobody is coming for you when you are pushing that tower or get an easy kill by placing it at their lizard/golem/dragon. It's also good to place a ward in the river to help you and your team from getting ganked as well as setting up counter ganks.

Manamune
Finally some more damage, By the time you get it it will give you about 50 damage, along with the mana and mp/5. Not bad, but! by endgame it gives 1350 mana so you will never have mana issues even when spamming. At level 18 when fully stacked you will get no less than 82 attack damage from this low cost item.(only 250 more than a BF sword)

Sheen
The first part of the almighty Triforce. Get this first to give the enemy a taste of what's to come.
Phage
The second part, health and slow? yessir.
Zeal
YOU'RE ALMOST THERE!


Finally, you can go win the game for your team. Trinity Force has so many stats that are good for you, its crazy. The most important part however, is that you will do insane damage with the 150% bonus damage on almost every attack. You can constantly use abilities during a fight with your mana pool and the 1.2 second cooldown on Missile Barrage ensures a lot of procs

Vampiric Scepter
I like to get lifesteal right after Triforce so I usually just pick up a vampiric scepter and upgrade it later. It helps to restore health on minions and jungle monsters and gives you a little bit of survivability in a fight.

Black Cleaver
Another key item in this build, it was reworked and has become awesome for corki
(This site shows the old Black Cleaver, the new stats are here: The New Black Cleaver).
A champion's base armor at lvl 18 is around 70 so that means that with 25 armor penetration from the runes and the 45 from black cleaver all champions without armor items will take close to full damage from your attacks and the Trinity Force bonus damage. The armor reduction also works for your team which is a huge bonus if you have more physical champions on your team. The 30% attack speed is welcome, especially if you bought Mercury's Treads.

Lategame

This is where the core build ends, by now the game will be in the teamfighting stage and you should be racking up the kills. The number one rule is: play defensively. I cannot stress enough how important it is to do so. I sometimes find it hard to do myself, greed will take over when I see that low hp enemy running away, but his teammate might be around the corner waiting to kill you. You are quite squishy and do high damage and they will focus you. It is important that you stay back and wait for them to engage your allies. if they decide to come after you, run away until they give up. When you are out of harm's way you can continue to pour it on 'em.

Lategame Item choices

It depends on the game what you should buy next.

If you cannot stay out of harm's way even with these summoners and valkyrie you will want to pick up a defensive item in order to stay alive during fights. Also in long games where you dont have trouble staying alive it is still wise to pick up 1 defensive item just in case. Burst damage gets very high lategame and the respawn time is long.

Banshee's Veil
Always a strong item against casters/CC and you get health and mana.
Frozen Heart
getting hammered by that tryndamere? Frozen heart will save you some trouble. The 500 mana also gives you 10 damage from manamune. 25% cooldown reduction, very nice!
Guardian Angel
I like to get this in very long games as one of my last items.

If you have no trouble staying alive, go ahead and increase that already OP damage you do.

Bloodthirster
Annoyed by that Vampiric Scepter in your inventory? Time to upgrade it!

Last Whisper
If they have multiple people stacking armor this will further reduce it, only needed against extreme tanks because you already have so much armor penetration.

Some info about MY PRECIOUSSSSSSSS.

There are many reasons why this build has the highest practical damage capabilities for Corki.
An ability power build is out of the question and could be fun to try once but will not give you nearly as much damage.
Some people might wonder why I didn't put Infinity Edge in my build.
Because of the high cost of Infinity Edge and Trinity Force and the different item paths they lead you on, you have to make a choice: Either maximize your Trinity Force proc damage or maximize your crit chance/attack speed/crit damage.
For many ranged carries an early Infinity Edge is the best way to become a high damage dealer. Corki is different, With this build he can spam spells all the time and make maximum use of the Trinity Force procs. You could say that he does 250% hits on a high percentage of his attacks. While with Infinity Edge the chance to crit is quite low at first, only increasing if you buy more crit items.

Some more advantages you get from this build over any other damage build:

Trinity Force offers a lot of different stats, movement speed is awesome. the 25% chance to slow is neat as well and it provides some health so you aren't UBER squishy.

Trinity Force has an internal cooldown system and it works like this: Each of your abilities has a separate 3 second cooldown. So you cast Q, then 1 second later, you cast W. At that instant, Q will have another 2 seconds before you gain the "on cast" effect, while W has 3 more seconds.
that means that you can use different abilities succesively to do a lot of bonus dmg hits in very short time. This is ideal because you can do a lot of burst quickly, then move when you get targeted until you are clear to deal another round of crazy burst.
If executed properly you can carry bad teammates quite easily.
The order would be R>attack>Q>attack>E>attack>R>attack.

The early item choices make sure you can farm to your heart's content and carry on to be useful during the whole game.

Trinity Force procs are not random. You can control when you want to do 250% crits, this means that you have superb poking power. Shoot 1 rocket at them and attack once, repeat this and you will tear their hp bar to shreds before the fight is initiated(only when you are sure that you are safe to be in auto attack range).

Damn, I spent a long time on this guide! Stayed up all night just so you guys could have a good read and learn a thing or two so I hope my efforts weren't in vain. Have fun playing Corki and winning almost every game! Feedback is welcome and I will try to answer any questions. If it turns out well I will add a few more things and I will try to listen to your suggestions. I will also add some of my match history to prove his viability.