Katarina is a very fun champion. She can dish out a massive amount of damage in a short time and has some decent escape tactitcs. She is fairly squishy however and does rely a little on the team in team fights. You need to cooperate with your team to use her to the full potential.

Voracity:
After a kill or an assist, Katarina gains 25 gold and her cooldowns are reduced by 15 seconds.

Bouncing Blade:
(Active) Katarina throws a dagger that bounces from enemy to enemy dealing magic damage. Each hit deals 10% less damage.
Leveling up: Maximum Bounces 2/3/4/5/6.
Leveling up: Magic Damage 60/95/130/165/200(+0.8 per bonus Attack Damage) + (0.35 per Ability Power).
Leveling up: Cooldown 9/8.5/8/7.5/7 seconds.
Range: 600

Killer Instincts:
(Passive): Katarina's abilities with a damage ratio and auto-attacks deal additional damage.
Leveling up: Damage increase 8/12/16/20/24

(Active): Katarina's ability gain a bonus effect:
Bouncing Blade: For every target it hits, will deal full damage and apply 50% healing reduction for 10 seconds
Shunpo: Katarina will take reduced damage from enemy attacks for 3 seconds
Leveling up: Damage Reduction 15/20/25/30/35%
Leveling up: Cooldown 20/18/16/14/12 seconds

Shunpo:
(Active): Katarina moves to her target's location. If the target is an enemy, she deals magic damage to the target.
Range: 700
Leveling up: Magic Damage 80/120/160/200/240 (+0.75 per ability power).
Leveling up: Cooldowns 10/9/8/7/6 seconds

Death Lotus:
(Active): Katarina goes into a state of extreme focus, throwing many daggers at the 3 closets enemy champions in 3 seconds.
Area of Effect: 550
Daggers Thrown: 30 (Max per Champion:10)
Leveling up: Magic Damage 50/65/80 (+0.5 per bonus Attack Damage) + (+0.25 per Ability Power) per dagger
Leveling up: Cooldown 60/55/50

Death Lotus:
-Can only be used when a enemy champion is in range.
-becomes usable evn if the only champion in range is stealthed.

Exhaust-this summoner spell in my opinion is a must on Katarina. It helps get so many early game kills its as if its made for her.

Ignite-This helps a lot as well early on and is nice against pesky healers.

Clense-I only recomend this if you are planning of getting Mejai's Soulstealer for better Surviverability. (Also I recomend to go with the 9/21/0 Mastery Tree if you like to go with the snowball items.)

When I play Katarina I go either 21/9/0 or 9/21/0 in the Mastery Trees. If you have noticed I go with [Nimbleness] in both of my builds. I am a big fan of it and just cant stop using it on Katarina.

As a Katarina fan I am sad seeing others start with [Shunpo]. The reason why is because they just try to harass with it and get themselves to take more damage than they do. Also many times it just puts them in the unsafe zone and they give away first blood. I find it much better to start with [Bouncing Blade]. This makes early harassing easy and you will be able to just get [Shunpo] at level 2. Even though I get [Bouncing Blade] first I still max out [Shunpo] first. After that I prefer to max out [Killer Instincts]. This helps reduce damage even more if you combine it with [Shunpo] or cripple healing if you pair it with [Bouncing Blade]. On top of that it still gives you bonus damage with its passive. Also I do not max out [Bouncing Blade] first because I prefer having [Shunpo] up as fast as possible for more mobility. This way you can use [Shunpo] to get away by using wards, minions, Teemo's Shrooms, Shaco's Jack in the Box, Jungle Beasts, Heimerdinger's Turrets, other Champions ally or enemy, and anything else I may have forgotten that is targetable.

My runes depend on the Master Tree and Item Purchases I plan to make.

21/9/0

[Greater Mark of Insight] (the magic pen is a nice bonus
[Greater Seal of Evasion] (the dodge helps to get [Nimbleness] active)
[Greater Glyph of Celerity] (the cooldown reduction is quite nice so you can use Death Lotus again after two to three kills)
[Greater Quintessence of Swiftness] (the speed bonus helps a lot if you get [Boots of Speed] and three [Health Potions]

9/21/0

[Greater Mark of Potency] (Helps your ability power early on with the Mastery bonuses)
[Greater Seal of Evasion] (Once again helps to get [Nimbleness] active)
[Greater Glyph of Celerity] (Once again helps your Death Lotus)
[Greater Quintessence of Swiftness] (Once again helps your mobility

My Item Purchases sometimes vary also on the [Mastery Trees] and I am planning of using. I also switch it up a bit and use some of the items with the other [Mastery Tree].

21/9/0

Mercury Treds-I tend to go with these because games seem to always have a lot of CC.

Hextech Gunblade-this item is now my favorite on Katarina. You can [Shunpo] in on a target use the active and unleash [Death Lotus] for a quick kill. Also if they seem to get away don't forget that you can use [Exhaust] and [Ignite] while using [Death Lotus].(make sure not to try that with the [Hextech Guneblade] active because you will interupt your [Death Lotus] You only usually need to do this if its a 1v1 on the map. When it comes to team fights it tends to be better to save the active for the runners after [Exhaust] wears off.

Rylai's Crystal Scepter-This is another great item for Katarina. For one you gain health. Second you get another slow. Now its even harder for them to run away from your [Death Lotus] and you can save your active from the [Hextech Guneblade] and [Exhaust] for the runners that are almost dead or to help you escape if you get hurt to bad.

Rabbadon's Deathcap-This just helps your burst severely and is a scary item since you already have a decent amount of Ability Power.

9/21/0

Ninja Tabi-I tend to get this item because I also take [Clense] so I usually don't need to get [Mercury Treds]. However if you just seem to need it you can trade it out later.

Mejai's Soulstealer-I normaly do not prefer to get snowball items because it puts a target on your back and matches are usually not easy to predict how they go. However if you wish to go with it be my guest. If you do not wish to get it you can also just go with the [Hextech Gunblade] Like with the other Mastery Tree.

Rylai's Crystal Scepter-Once again I suggest getting this item because it helps with your surviverability and adds an extra slow. Plus if you have [Mejai's Soulstealer] you will want this since you do not have the [Hextech Guneblade] active

Rabbadon's Deathcap-I love this item because it makes you so powerfull. Once they think they know how powerfull you are you sudenly just burst them down with little to no effort and blow their mind.

I start out with [Boots of Swiftness] and 3 [Health Potions]. If they have a Jungler I usually request the side with [Blue] on the other side of the river and grab a [Sight Ward] instead off 2 [Health Potions]. I ward [Blue] if its safe. If you dont want to go throught the grass behind [Blue] because you are afraid of getting ganked just go the front and ward it just close enough to show Blue. If the jungler uses [Smite] right away instead of waiting to last hit it with Smite just steal it with [Shunpo] or [Bouncing Blade]. This takes some timing but its not to hard once you get the hang of it. After that just take out the jungler quickly and move on before the others come to help him or cut you off.

Anyways if you didn't get the chance for a free [Blue] just be aggressive if it allows and don't forget to use your Health Potion as you enter the fray that may hurt you quite a bit. Just make sure you don't wait to long to use it or you will just get killed or be forced to let up on the attack early. If you use it as you enter the fight you will have an advantage over the others because you are gaining health as you are loosing it. Timing this to the fullest potential takes maybe some practice but its effective against those that use it to late. Just be aware of who has [Ignite] on the other team or you will be in trouble if not carefull. With 3 Health Potions you will have 600 extra health if you time your health potions over the 100-120 health from the Dorans items.

21/9/0

After some time of last hitting minions or getting a few kills on the other team my first item is the [Bilgewater Cutlass]. I get this first because it gives you bonuses to your [Bouncing Blade] and [Death Lotus]. Also the life steal and bonus attack damage helps a lot when your abilities are down. The reason I do not go for Ability Power right away is because the base damage of [Shunpo] already will be doing a good amount of damage at this time and your [Bouncing Blade] is still a little weak at this point so the Attack Damage will at least power it up and [Death Lotus]. Besides the [Hextech Gunblade] is not to far off after this. A good idea if you have enough money is to get the [Giant's Belt] before getting the [Hextech Gunblade]. Extra health is always good early on.

9/21/0

If you are going with the Defensive Mastery Tree the first item is of course [Mejai's Soulstealer]. Getting this early helps get stacks early. Also if possible I get [Giants Belt] from [Rylai's Crystal Scepter] soon after for more health. This helps cancel out your weak health a lot.

21/9/0

At this point I start making sure I get [Hextech Gunblade] and [Ryalai's Crystal Scepter]. If Possible I start getting items for [Rabadon's Deathcap]

9/21/0

Since this build is cheaper than the other you may already have [Rylai's Crystal Scepter] and have already begun saving for [Rabadon's Deathcap].

Team Fights

Aside from getting these items you now usually start the team fights. One very important thing is to watch your opponent and see what abilities they use. Once you see the interupts for your [Death Lotus] used and are on cooldown it is a good idea to find a good time to jump in and use [Death Lotus]. This comes easier the more you play and learn what each champion does. You will have to do this for the remainder of the game./color]

If you reach this point and you still do not have [Rabadon's Deathcap] you really need to pick up the pace. If the reason is that you get focused as you use [Death Lotus] try to communicate with your team and tell them what is happening so they can stop it and get more damage out of you.

Banshees Veil-this item is great if someone just saves their interupt for [Death Lotus] just for you. It blocks one ability so its a helpful shield for you.

Void Staff-this is a great item if the enemies are getting some magic resist to combat your damage.

Lich Bane-this is a fun item on Katarina because by the time you get this you will have around 600 ability power and the unique passive effect will do around 700 damage with your next auto attack.

Guardian Angel-if the other team just seems to hate you so much that they just kill you in team fights this might be a good idea. Even when you use [Death Lotus] once and at least get two assists you can jump back in to follow up with another [Death Lotus] by the time it revives you.

Deathfire Grasp-this item is great on champions that have a lot of health but little magic resistances. You can just open up with it and then go in for the kill. (Great item against Vladamir)