Voracity

When you kill an enemy or get an assist for an enemy death, you instantly gain 25 (used to be 50) gold and your abilities cooldowns are reduced by 15 seconds. One of the best passives in the game, allows you to pick off a target and instantly shunpo away. Your ultimate requires about 3 kills/assists to completely go off cooldown.

Bouncing Blade

Great early game skill. Scales with your attack damage, so it grows as you stack your attack damage. In the early game, use this to last hit creeps and also harass champions, giving you a health advantage to go in for an easy kill. It bounces 2/3/4/5/6 times as you level it up.

Killer Instincts

A decent skill that passively adds damage. When activated, gives either your Bouncing Blade or Shunpo a bonus effect. With Bouncing Blade, it hits for the full damage on every hit (useful for harassing) and for Shunpo it makes you take reduced damage (OH YEAHHHH)

Shunpo

What can I say about this ability? A teleport and a damage ability in one. With a low cooldown to boot, be prepared to be using this spell alot to kill, jump in, or to escape. Combine with Killer Instincts in a team fight to take minimal damage. This scales with AP, so with an AD build don't expect this to do tremendous damage.

Death Lotus

Pretty strong ultimate. It scales with either AD or AP (whichever is more) so it's not recommended to build both. At rank 1, it doesn't do as much damage as you'd hope, however its still better than auto attacking. As you stack up attack damage (like I recommend in this build) you will notice that enemy champions drop down much faster.

Katarina is a great character to play. She dominates mid with little to no exception. She is an amazing asset to your team in a team clash, decimating enemies with her Death Lotus and if untargeted, can score triple/quadra kills with ease. However, she lacks a slow or CC and is squishy if targeted first. In this guide I will cover both conventional AD builds and AP builds, both of which are viable.

Pros:
Can lane mid effectivley
Can decimate entire teams
Great early game, Great late game
Moderate difficulty to play
WATCH HER SPINNNNN
Cons:
Has a lame dance
Low attack speed makes for spells being priority
Squishy, nuff said.

AD:
- Auto attack damage increased, therefore you don't deal crap damage on turrets
- Generally cheaper to build more damage early
- Bouncing blades hit more than ONE target, making it easier to clear out enemies
AP:
- With Rylai's, all 3 of your abilities including Death Lotus will slow the target
- Generally, AP Kats have more HP than their respective AD kats
- with 40% CD reduction, which is easily obtained through masteries and runes, Shunpo's cooldown is at 3.6 seconds, making it a very low cooldown used for finishing off champions and getting away.

For masteries I run a 21/0/9 getting AP/level, CD reduction, Spell Penetration, Armor Penetration, and everything up to Havoc. In the utility tree, I get reduced death time, and EXP along with 1 point into greed.
Another good option is 21/9/0 instead by grabbing armor, magic resist, dodge and nimbleness. I have great success with both.

However, if you're going for an AP build, your masteries will be 9/0/21, grabbing spell pen in offense and getting all NON-MANA related masteries in utility.

For runes I use
Flat Magic Penetration Marks
Flat Health or Dodge Seals
Flat CD reduction Glyphs
Flat HP Quints
Although, Movement speed can also be used for the mobility.

When the game starts on Summoners Rift, grab a Boots of Speed and 3x Health Potion
This assures you have the mobility in the early game to dodge any skill shot based abilities such as Morganas Dark Binding or Ezrael's Mystic Shot. Also, the mobility helps boost your ability to weave in and out of combat last hitting creeps and harassing enemy champions.
Your next key items are simple enough.
B. F. Sword, Mercury's Treads
This is simply a godsend for Katarina. This adds 50 damage to your Bouncing Blades. Also, with this 50 damage, your Death Lotus now does about 25 more damage per dagger. Stacking BF swords is simply the best way to pick up damage quickly.
Mercury Treads assures that you can survive the big nukes and stuns.
Usually after the second or 3rd B. F. Sword, you will want to change it into The Bloodthirster.
Stacking Bloodthirsters after your 2nd or 3rd BF sword is simply the best way to boost your damage.
Now, before stacking your Bloodthirsters, you might think "Oh dear im squishy like crazy, how will i survive?"
Let me tell you 2 things that will help you:
1) Banshee's Veil
Yes, it does have mana, but the health, magic resist, and amazing passive assures that one stun will not throw your ultimate off.
2) Elixir of Fortitude
Always, ALWAYS have one of these on you. These simply guarantee you have a good health bonus and damage bonus to be able to gain a huge advantage on enemies early game.

If, after the 3rd BF sword and a Banshees veil, the game still goes on, grab a [item=Divine Rapier]... wait a second...
:D
Grab anything that suits your preference. If you want more damage, grab another Bloodthirster. If you want more survivability, grab a Frozen Mallet which will help ensnare enemies as well as give you a whopping 700 health bonus.

For the AP build:
Start the game the same way, Boots of Speed and 3x Health Potion.
This assures you have mobility to weave in and out of combat, making you very nimble and mobile. However, Amplifying Tome can also be a good starting item.
You're going to want to get Haunting Guise and the Spell penetration shoes first, as You will be able to penetrate most of the enemies defenses early game. After these 2 items, your next item will be the famous Rylai's Scepter so that you have a slow on each and every one of your abilities. This is the "core" for Katarina, meaning that these 3 items are THE MOST important for her. Afterwards, you want to buff your AP even more, however, you need to look at what items will help you better. If your enemies are stacking Mresist, and they have alot of casters, kill 2 birds with one stone and grab
Abyssal Scepter since you are always in the middle of the fray.
If you want flat out AP and a nice little active if things don't go your way, grab Zhonya's Ring.
If you want flat out AP, and a nice little passive that gives you a nice extra on your auto attack every time you cast a spell, get Lich Bane. Note, only get this once you get over 200 AP (without this item)
If you see that tanks are starting to get more HP, or that people themselves are getting more HP and you want a nice little active that takes care of that, along with an awesome reduction in your cooldowns, get Deathfire Grasp.
If people are starting to get REALLY high in their Mresist, grab a Void Staff to ruin their day !
If no other caster gets this, it's the equivalent to starks fervor for casters
Will of the Ancients

Please do not think you have to follow this skill build word for word, this is how I build my Katarina.
AD build
1.) Q
2.) E
3.) Q
4.) W
5.) Q
6.) R
7.) Q
8.) E
9.) Q (maxed)
10.) E
11.) R
12.) E
13.) E (maxed)
14.) W
15.) W
16.) R (maxed)
17.) W
18.) W (maxed)

Basically, you want to get Bouncing blades to 5 as fast as possible as it is your main damager and harasser through out the game. Killer Instincts at level 4 assures that you have the added abilities to counter enemies. Shunpo is next as it is your other damager and putting it at a lower cooldown by upgrading it is the best choice.

For the AP build
1.) Q
2.) E
3.) E
4.) Q
5.) E
6.) R
7.) E
8.) W
9.) E
10.) Q
11.) R
12.) Q
13.) Q
14.) W
15.) W
16.) R
17.) W
18.) W

This build focusing on maxing your AP move, shunpo, first. It also gets a few ranks of bouncing blade early so you have 2 nukes instead of just 1.

With Kat, I run Ignite and Flash
Why do i use Ignite and Flash?
Ignite: Assures that you have that finishing touch on an enemy as they are running away. Early game kills will be assured by this. Can counter enemy heals when you feel confident to kill them. This has a million and 4 uses that can't be written here.
Flash: "OMG YOU HAS SHUNPO NOOB WHY NEED 2 TELEPORT?! LOL NOOB" Alright, Flash almost assures you have 2 ways to get out of any situation. Need to close in some distance between you and an enemy to shunpo? FLASH. Need to close in to a teammate to make it out alive? FLASH. See what I mean? I use this over ghost since Flash is jerky. Its sudden. You don't know someone flashed till they're pounding on your backside.
Ghost: Even if I don't use it, Ghost is still very viable.
Exhaust: Alright, Exhaust is also a very good option, but I'd rather give it to my teammate.
Cleanse: Very good skill for Kat, ever since the nerf I don't use it much, but its still good.
Heal
Teleport
Are also good choices.
DO NOT GET
Revive (dont ask)
Rally (you don't stand around long enough to gain its advantage)
Clarity (get out)

You will never be the first one in. Ever
You will be somewhat the 3rd or 4th. Let your tank/initiator go in, soak up some disables. Use killer instincts, position yourself in the middle. Throw a bouncing blade and then let loose with Death Lotus. You might need to flash out and then shunpo back in to finish off any runners. Otherwise, just keep going till death lotus is finished and then chase and finish off when needed.

Farming with Katarina is very easy, just use your spells shunpo and bouncing blades to score last hits. Having no mana means that you can comfortably spam your spells.

The common question you might get asked is: "Katarina do you want mid.?"
What you should ALWAYS look at before answering this question:
If I solo, who will i lane against? --> Do they have any stuns/disablesnukes that might hinder farming?
If someone else solo's, who will my lane partner be?
Do I have a good teammate that can assure we can farm safely and score some kills on the side?
Is someone else more suited to getting their ultimate faster?

Its your call on this, but i'd rather let that Karthus or Heimerdinger or even Mordekaiser if they can be trusted and since each of these classes are more suited to getting levels faster.

I have played Katarina many, many, MANY times and have found she is extremely entertaining and a very potent character. Both the AP and AD builds are viable, however, I use an AD build myself.
Enjoy playing Kat, if you have any questions, message me on EU or US servers as: Brokenshard, or simply add a comment.
See you on the battlefield!