As we all know Katarina is a very played character and is considered to be OP. So lets take advantage of it. Here is my guide to success using Katarina. Around 90% of the Katarina's I have faced are bandwagoners they play her because she is OP. Now using my guide you will not be a bandwagoner but a more skilled player. I hope you enjoy my guide and if you want to add me my IGN: whosJakee Thanks!

First buy boots and three pots which is standard for almost any build of Katarina. On your first trip back to shop buy Spell Vamp with Hextech Revolver. After you farm and hopefully gank, you should come back to the shop with enough money to buy Sorcerer's boots. These will give you more significant damage later on in the game. After the boots, if you are having trouble catching your opponents, build Rylai's Scepter. If you are fine with catching, but you can't seem to do enough damage, build Rabadon's Deathcap. In my opinion, I do not think that Hextech Gunblade is worth the gold. Instead, build Liandry's Torment. This will give you bonus damage and a burn effect that will continuously irritate your opponents. Next, if you haven't won the game, build any kind of magic penetration, such as Abyssal Mask or Void Staff, or get more AP, such as another Rabadon's, or Zhonya's Hourglass. That's all for items!

Pros

Early Harassment No Mana Needed Ability Similar to Flash Strength at Lvl 6 Great for teamfights Amazing Lane Farming Huge Breasts

Cons Squishy Early game Useless without abilities Cooldowns are long Easily Countered with silence

The reason the runes I put up above are most effective for katarina is because all of her abilities deal extra damage depending on her AP. Starting off with more AP is always good, considering Katarina is a little squishy until she is level 6. Many Mids will often build magic resist to counter katarina so magic penetration makes sense as a rune to use. I use armor because early game everyone does around the same attack damage and since Katarina is a melee she needs armor if she wants early game CS. She also needs a decent amount of armor to survive early game ganks and stay in lane. The Quintessences are explanatory since this is a AP build and the AP Glyphs as well.
Here is an example of what one might use.

Here is a little video for newer players wanting to see the abilities in action (and their description which is more helpful) Play Video
Thanks HugeBuffaLoL For the Video!
Katarina's Passive Ability: Voracity Voracity
After a kill or assist, Katarina's abilities cooldowns are reduced by 15 seconds.
Kat's Q Ability: Bouncing Blades
Cooldown: 10/9.5/9/8.5/8
Description: Throws a blade dealing 60/95/130/165/220 (+45% of Ability Power) Unique Passive: Leaves a mark on the targets hit allowing the next spell to deal 15/30/45/60/75 (+15% Ability Power) Magic Damage.
Kat's W Ability: sinister steel
Description: Whirls daggers in a circle dealing 40/80/120/160/200 (+0.6 per bonus Attack Damage) (+25% of ability power) magic damage. If she hits an enemy Champion, Katarina gains 12 / 20 / 28 / 36 / 44% Movement Speed for 1 second.
Kat's Q Ability: Shunpo
Description: Katarina moves to her target's location, appearing behind it. If the target is an enemy, she deals 60 / 85 / 110 / 135 / 160 (+40% of ability power) magic damage to the target. After using Shunpo, Katarina gains 15% damage reduction for 3 seconds.
Kat's Ultimate: Death Lotus
Description: Katarina throws a flurry of blades, channeling for two seconds and sending up to 10 daggers at the each of the 3 closest enemy champions dealing up to 400 / 500 / 600 (+ 3 per bonus attack damage) (+175% of ability power) magic damage over 2 seconds to each champion. Daggers that are thrown apply Grevious Wounds, reducing healing and regneration by 50% for 3 seconds.

Skill Sequence is always a debated topic for Katarina. I perosnally think that Q is the most effective to upgrade the most, because you can harass from very far away. I always get one of each first, started with q because many noob mids stand next to their minions, causing Bouncing Blades to hit them (target the ranged minions). I then get Shunpo because at level 2 using q then shunpo deals a good amount of damage. And by making the enemy afraid of you by shunpo'ing in you have thus given yourself enough time to escape from melee combat. Many do not realize that the bouncing blades give you extra damage on your next spell (hence the little knife above the character). And because I upgrade my W sinister steel most, I would suggest using it to damage and mark target first and quickly use shunpo and lastly follow up with sinister steel (ult if low enough).

Teamwork is a big deal when using Katarina because she is almost worthless wihthout abilities. In a team fight always be cautious as to how much health the enemy team has. You never want to jump into a fight without the ability to kill someone. I always harass until i can be sure i will get one kill. Many teamfights i have seen to be failures because a Katarina dives in and uses her ultimate with a full health 5v5. Katarina is a cleanup crew.
This means that she comes in later and takes all the kills. It may seem a little unfair but if she is fed and gets all the kills the game has been won. Every time Katarina gets a kill her other abilities refresh, so using her ultimate right after using q,w, and e is probably the best strategy. Then use the same tactic i described in the skill sequence once again. If you join a teamfight at the right time, or even just poke with bouncing blades it can mean the difference between winning and losing a potential teamfight. P.S Always be aware of your team's abilities and strengths so you know which enemy to target first or when to attack that target.

Many characters in game are almost useless in 3v1 4v1 5v1, not Katarina. Let me give you two situations and advice in what to do in them.
Situation 1: You are in midlane without wards early game and a just the jungler comes for a gank while you are to close to tower.
Advice: The minute you see a gank DO NOT RUN. Stay calm while checking map position of your minions. If there are minions coming your way from tower do not be afraid to poke with a q and a w. I suggest not wasting flash or attempting a 2v1. Use shunpo to get away from the enemy once you see them going in for the kill. If there are no minions around do not necessarily run to the turret. If you have lowered the enemies health run to the opposite bush of the ganker to your nearest jungle or even the next lane.
Situation 2: You are ganking bottom or top lane to support tower in a 4v2 situation where your ally at the lane is low health and baiting them into tower.
Advice: Signal the laner to stay near turret and have damage done to the opposing champs. Come into the bush in the river and wait until they have pushed/killed your ally champion enough. Come into the battle with a q first, shunpo to a minion or low health champ, w for damage and then ultimate. Always attempt to kill the weakest character first because your abilities will regenerate. You may be able to take out a 4v2 in a matter of seconds.

Despite Katarina being overplayed you may be able to have the advantage by playing skillfully and carefully! Have Fun and Good Luck All of You!