THIS GUIDE DOES NOT GUARANTEE VICTORY NOR DOES IT GUARANTEE GETTING A GOOD SCORE
Have Fun! Remember that this is a game!
Katarina is a powerful nuker, however squishy almost all the time. She can mid or lane fine with either build. I recommend the Flash build for top/bot as having Exhaust is useless as the other champion can kill you. While midding taking the Exhaust to easily kill or push the opposing mid out of lane.

Pro
-Heavy AOE Nuke with Ult
-Doesn't worry about spells getting wasted, she has no Cooldowns
-Killer Instincts allow you to take less damage
-Free Flash allowing you to avoid skill shots
-Good Ganker
-No Skill shots! YAY!
Cons
-Extremely Squishy
-If not careful crowd control will kill you instantly

Scores from when Hextech Gunblade could stack

Anyone with a stun, fear, silence, knock back, knock up, taunt or suppression. They will interrupt your ultimate. Make sure it was used or it isn't being used on you while you're using Death Lotus
Here is an example of stun/fear/silence/knock back/knock up/taunt/suppression champions.
Stun
Fear
Silence
Knock Back
Knock Up
Taunt
Suppression

Magic Penetration reds allows you to deal more damage to your opponents with magic resist.
Flat ability power yellows gives you great early game damage, you may to swap them for flat HP for stronger early game, scaling HP greater seal of vitality for decent health throughout Flat armor works as well but you would have less Magic Resist, so I would advise pairing it up with Flat Magic Resist glyphs, if you chose to take tankier runes.
Cooldown reduction blues good cooldowns for the whole game. Good farming and easy kills. If you find that your early game is strong enough and that your late game is too weak, you may swap them for AP per level . Flat Magic Resist, to be able to take more damage. Paired with flat armor seals.
Flat AP Quints are the same as blues. Giving good early game. You may swap for Flat HP or AP per level .

22 points in the offence tree to maximize damage in all stages of the game.
8 points in the utility tree for less death time, and more move speed.

- Voracity-Every kill or assist grants 25 gold and cooldowns are reduced by 15 seconds.(Not summoner spells)This is what makes her cooldowns not much of a problem.
- Bouncing Blade-Bounces 2/3/4/5/6 times on enemies, does not hit a target more than once. Great farming and harassing tool, has a lower range than Shunpo but doesn't teleport you. Range 600
- Killer Instinct-Adds extra effect to ability. Bouncing Blades-Deals full damage to all targets hit and lowers regeneration by 50%. Shunpo-Damage reduction by 15/20/25/30/35% for next 3 seconds. Lets you Shunpo in and take less damage or reduce the healing of those like Mundo.
- Shunpo-Also good farming and harrasing, heavy single target damage, Teleports you to target (friend, foe, champion placed objects but not turrets) Range 700
- Death Lotus-AOE nuke. Throws 10 blades that hits up to 3 of the closest enemies. Big AOE damage. Perfect for team fights with enemies who don't move. Can hit stealthed champions, will show up as available to use when they are in range. Range 550

8 Wards are put at max radius to show you the relative distance to warding.

Wards

Bouncing Blade

Shunpo

Flash

Death Lotus

As shown, Shunpo has the greatest range and is a "Flash"(Note: Shunpo/Shùn bù 瞬歩 means Flash Step in Japanese and Chinese). A person with great micro would be able to place a ward over a wall and use Shunpo to it getting away from someone.

The 1st build maxes Shunpo first for heavy single target damage (farms well), also you don't have Flash so its always nice to have a free Flash. Grabbing a quick point into Killer Instincts allows you to nuke your opponent while taking less damage.
The 2nd build takes 3 points Bouncing Blade first for farming and easy harassment. Again grabbing a quick point in Killer Instincts granting better survivability. After you get your ultimate you should focus on maxing Shunpo for the instant damage while jumping into a team fight.


The basic combo of jumping in to kill someone is Killer Instincts- Shunpo(to your target)-Death Lotus -Exhaust(if you have it) -Ignite . If you run into trouble while in that fight Shunpo /Flash out.
If someone who has massive HP regeneration (like Dr. Mundo) use Killer Instincts -Bouncing Blade to halves their HP regeneration similar to Ignite and (if you can) finish them off with your basic combo.
Picking up a kill is as easy as pressing Q-W-E-R-D-F. However when playing with people who know how to interrupt your ultimate be very careful as they will most likely do so. Knowing when to push all the buttons and when not to separates the good Katarinas and the bad ones. Though she is easy to learn, she is hard to master.

Taking Exhaust and mastering it allows you to deal more damage with less worry about them running away. Using exhaust is also great for making an escape, as it reduces their damage and speed.
Taking Flash allows you to take a skill other than Shunpo to start with and is a great all around spell, also doesn't require a target like Shunpo does. Keep in mind its range is lower than Shunpo and its cooldown is much longer.
Ignite is great as it helps your nuke while also reducing their healing, also good for finishing off those people at low hp while everything is on Cooldown. I find that Ignite is essential with Kat no matter what build you take.

Other Summoner Spells
If you don't have flash and don't wish to take Exhaust.
If you can't take anything else. Though as a squishy it will heal you pretty well.
You shouldn't need it. Doesn't help your nuke. If you are dying too often you'll just get more deaths with this.
This build is not a jungle build. You should not have a problem last hitting minions as well.
Another good all around spell. Lets you teleport to anywhere including wards. However Shunpo can take you across the map if used repeatedly.
If crowd control is a big problem this would be a good choice. Although your ultimate would have already been negated.
Katarina not uber pusher, but super siege minions are pretty good.
Katarina has no mana...
Do you really want to be a pseudo Cho'Gath?
Nice spell that gives you vision, but then again your support should take it.
Another option as a pair of summoner spells is /

I start with boots and 3 HP pots to give me good mobility
Slows enemies with damage dealing abilities. Keep them in your ultimate just a bit longer.
Stack lifesteal and spellvamp allowing your spells and basic attacks to heal you, letting you stay on the battlefield for much longer. Will of the Ancients is a suitable replacement.
Capping your Magic Penetration a 49% to deal even more damage to those building magic resist.
A no brainer on all AP casters. Increases your ability power by so much.
instead of magic penSorcerer Shoes so that I can throw nukes down more often than they would think.

Lich Bane is a good item. However it is situational. It gives a move speed but your attack animation isn't the best. Also Katarina has no mana.
Blocks a spell that might be intended to interrupt your ultimate. Easily countered as they could throw a useless spell and then use crowd control on you.
Gives flat 20 magic penetration, if their team has a little magic resist built. For those who don't find cool downs a problem at all this is a good choice.
Assuming you grab a couple kills without dying, this would be a good item to get. At max stacks it gives more AP than Rabadon's Deathcap when excluding the unique passive. It also gives Cooldown Reduction at max stacks.

This is a good item in theory, but it alerts the enemy that you are nearby if you are hiding. Also a Void Staff will give more Magic Penetration and if both are used together it is more effective to use just a Void Staff if the target has high Magic Resist. You may as well take Sorcerer's Shoes instead as it does not reveal you. Gives nice Magic Resist along with the other stuff.
Good item, but it interrupts your ultimate. Not wise to take it. If you really want armor, grab something else.

NOTE:Fiddlesticks' passive is similar to this passive and reveals him. So grabbing Abyssal Scepter with him would be fine since he is already revealed. Also the Abyssal Scepter aura has a larger radius than Fiddlesticks' passive.

However most people I have encountered don't have the awareness to notice these aura debuffs. So use at your own risk.

Bouncing blade and Shunpo are great farming tools with a low cooldown. Keep in mind the casting range of Boucing Blades is not as far as Shunpo, but Shunpo teleports you to the location while Bouncing Blades won't move you.

There should be no need to take Red buff or Blue buff, unless nobody else on your team needs them.Red applies slow and damage but you aren't an AD champion though if you took a Lich Bane I can see Red buff be put too good use. Blue gives a mana/energy regen buff which you don't need, however it does give some nice cooldown reduction. If a teammate is in need of the regen buff don't take it. Although stealing their jungle can hurt their team and benefit yours. Red buff has been changed, it now applies the slow and true damage to single target spells. Therefore Shunpo now applies the red buff!
OK SERIOUSLY RIOT? Red buff once again does not apply to spells.

I don't recommend taking Katarina into a ranked game. She is easily stopped, extremely squishy, and has no base crowd control. Also in ranked games it is prefered to have a ranged character so that you're "Zone" is larger than those who are melee. This video explains zoning. Play Video I have tried Katarina in a ranked game getting a decent score, but then again I am in ELO Hell with all the trolls.

1) Wait for the enemy team to waste all their crowd control(or make sure not to get stunned if its a skill shot) before jumping in and using your ultimate.
2) 4 Hextech Gunblades does not equal God Mode. It is Semi-God Mode. Don't be over aggressive.
3) Prioritize using Shunpo before Flash as Flash has a longer cooldown and shorter range.
4) Cooldowns....wait what cooldowns?
5) STUN, SILENCE, SUPPRESSION, KNOCK UP, KNOCK BACKS, STOP HER ULT (I know I said it before but its important)
6)Use spells whenever possible, you have almost no cooldowns and no mana.

1)Rylai's will slow for the full amount for every dagger thrown with Death Lotus .
2)Death Lotus will be available to activate when champions are near you, including those who are stealthed.
3)Using Shunpo on a ward /sight ward reveals it.

8/15/11-Started Making Guide
8/16/11-Publish
8/18/11-Added "Items to Avoid" section, Added Chinese Art Shown Below, Fixed a few things
8/19/11-Minor edits with spelling or grammar, remade mastery chapter, edited items to avoid.
8/20/11-Changed up Rune chapter a little, changed the part where Abyssal Scepter was mentioned
10/2/11-Updated Item Build, Tweaks about items in some sections,New Score added
12/18/11-Updated part about the red buff
1/19/12-Updated Red Buff part...AGAIN, Minor Tweaks