Hey! So this is how I build/play Katarina. It is based around AP because of what I concider her main nuke, Shunpo. Her other skills also gain from ability power, but this skill does not gain from Attack Damage, so it does not make sense to me to build her with attack damage. Later I will get into different skill combos and styles of play, but for now we can leave it at this. :)

Pros:

No Mana
Great Finisher
Insane Aoe Hero Damage
Great Harasser

Cons:

Poor survivability if you are reckless

Recommended:

This is one ability that I personally like a lot. It can be used to get to a teamfight faster, to sprint to another lane to gank before they even know you are gone, to escape a really bad situation, or just to get a little boost to get into Shunpo range. The possibilites are (almost) endless.

This is another great ability with all different kinds of uses. You can use it to escape over a treeline, close the gap between you and a target for a Shunpo, or whatever else you might want to do with a blink.

Alternative:

Some people like to use this ability to get some kills early game, and to apply the healing debuff as well as some extra damage late game, but I don't like it. I'm not saying this is a bad summoner spell, it just doesn't fit my playstyle. You have the same healing debuff from your Bouncing Blade, and getting a final hit on someone is usually not a problem with Kat. This is by no means a bad choice as a summoner spell, but just remember that if you do take this, do NOT get the mastery for it, instead put one of the points from the utility tree (whichever spell you decide to not use) into Greed for a little extra money.

This is another option for Kat. If you are afraid of getting stunned/silenced to death, this is a great summoner spell. It lets you clear everything and Shunpo / Flash out of danger.

Some people like to take Exhaust with Kat, but I am strongly against it. The problem I have with it is that once you get your Rylai's Crystal Scepter, I feel like it becomes an almost useless summoner spell.

Looking at each of the different "types" of runes, you can see that each one gives a higher yield depending on the stat/rune combination. Basically, each rune "type" is itemized better for certain stats. This sounds confusing even as I am writing it, so allow me to explain with some examples.

Ex. 1: Marks give .95 Magic Pen, but Glyphs only give .57
Ex. 2: Glyphs give 3.06 Ability Power but Marks only give 1.8

So when you are trying to get the most out of your runes, try to pick ones that are itemized for the specific rune type. Some good ones to choose from are Magic/Armor Pen for Marks, Health/Armor for Seals, and Cooldown Reduction/Ability Power for Glyphs.

Greater Mark of Magic Penetration: All of your attacks, including Bouncing Blade and Death Lotus, deal magic damage. This should be the only Mark you use.

Greater Seal of Vitality: This is the Seal that I prefer because I am not a big fan of dodge since it doesn't work on spells, and the health boost is just all around good.

Greater Glyph of Scaling Cooldown Reduction: I only get one of these because with the Ionian Boots of Lucidity, Mejai's Soulstealer, and your masteries, this will put you at 39.9% Cooldown Reduction at level 18, assuming you have full stacks. Of course you could just get another Ability Power Glyph, but .9% Cooldown Reduction is better than 3 Ability power in my opinion (although it probably wont make a difference either way lol)

Greater Glyph of Scaling Ability Power: This is pretty straight forward, you want to max your damage and this gives you more damage.

Greater Quintessence of Magic Penetration: I choose magic pen quints because this starts you off with around 14 Magic Pen, which is enough to put the hurt on enemy heroes even before you get you Void Staff

Kat's Passive! It is so good I cant even start to describe how good it is lol. What this does is every time you kill a hero or get an assist, ALL of your cooldowns are reduced by 15 seconds. Keep this in mind when you are in a fight because if you see some1 with low health, ALWAYS Shunpo them, then Shunpo to some1 else, throw a Bouncing Blade, whatever you want to do. Oh and u get 25 extra gold, nothing wrong with that.

This is Kat's main farming ability, as well as her main harass ability. It throws a dagger that does decent damage, as well as bounces to other target, dealing 10% less damage to each target it hits (unless Preparation is used, which causes it to deal full damage to each target it hits.

This is an ability that gived added bonuses to your other abilities. For Bouncing Blade, it causes each bounce to still deal full damage, as well as apply a 50% healing debuff to each target it hits for 10 seconds. When used with Shunpo, it causes you to take 15-35% less damage (based on level) for 3 seconds after using Shunpo. This is good for shielding yourself during your Death Lotus.

This is your best ability. Make friends with it. It can be used to escape a bad position, engage an enemy, catch running enemies, and to last hit creeps extremely reliably because of its huge damage.

Your beautiful ultimate. This is what allows you to completely destroy an entire team, but also what can open you up to insane amounts of hurt urself. If used incorrectly, you will end up doing zero damage and just dying.

The reason I get Bouncing Blade first is for two reason. 1) You can throw a dagger to help your jungler get some free damage on his creeps as soon as they spawn and not miss any xp, and 2) it is great for last hitting creeps and staying back. Although you can also use Shunpo to last hit, I try not to because it puts you right in front of the enemy champion and can open you up to some unnessecary damage taken.

I also tend to not get Preparation until level 13 because it doesn't do anything on it's own, it simply buffs your other abilities. This can be situational though, if you fight an enemy that has extreme healing capabilities, Ex: Dr. Mundo, u might want to take this skill around level 8 in order to apply the healing debuff to him.

This is by far the best way to start off as Kat. You are not an early game hero, so getting an Amplifying Tome and one Health Potion gives you less time in the lane to soak up all of that valuable experience.

I really prefer these boots over the Sorcerer's Shoes for two main reasons. 1) You are cooldown based hero, and these give you exactly that and 2) with the Marks and Quints I have chosen, the Sorcerer's Shoes would just be overkill. There is also the option to get Mercury's Treads if you feel you are being stunned/silenced quite a bit, but you are going to lose out on almost all of the Cooldown Reduction available to you early game so I do not recommend it.

I try to stay in the lane until I get at least 1900 gold before I leave for the first time so I can buy this and the boots at the same time. By now you most likely have used up all of your Health Potions, so once you get these items it will allow you to spam your Bouncing Blade and Shunpo in order to keep you alive instead of having to gobble up tons of potions (and gold).

Most people are against items that snowball, but in the correct situation it can be a game changer. The reason I don't get this before the Hextech Revolver is because in order for this item to be good, you need to be able to gauge the flow of the game. If you get to this part of the build and you have been getting a few kills/assists, this is a great item to pick up and punish the enemy team. If you have died a few times, or ur teamates aren't doing to well, I would suggest skipping this item and going straight for Rylai's Crystal Scepter.

This is probably the best item in the game for Kat. It gives a good amount of health and AP, as well as an amazing passive. Whenever you throw your Bouncing Blade, it applies a 15% snare to every target it hits. What is even better, when you Shunpo to a target, they get a 35% snare applied. The reason this is so good is because you can Shunpo to a target, and then activate your Death Lotus. This literally gives then zero chance of escaping your Death Lotus (unless saved by a partner or summoner spells), giving you insane killing power.

I'm not sure how to explain why I got this item other than... ABILITY POWER OM NOM NOM.

Ok so if you get this far into the build and the other team hasn't /surrender'd, they should have at least one person on their team with over 100 Magic Resistance, as well as a few other heroes with semi-decent resistances. This item will rip through them like they ants because combined with you mastery for 15% magic pen, this stacks (multiplicatively) giving you 49% magic penetration.

The only reason that you would get this item would be if earlier in the game you did NOT get the Mejai's Soulstealer or you are fully built and have died a few times, resulting in your stacks falling extremely low. This item will allow you to reach your max cooldown reduction while giving you some AP, along with a very nice active for taking down someones health before initiating (at the end of the build this can take off roughly 50% of someone's current health lol).

The games rarely go this long, but by now you would have you entire inventory filled up, and you only have one item that can be built further, your Hextech Revolver, which can only build into two different items, Hextech Gunblade or Will of the Ancients. The way Kat's abilities work, she gains Bouncing Blade and Death Lotus damage from BOTH Ability Power and Attack Damage, so the Hextech Gunblade is just better in every way.

If the game ever goes past the point where you have fully built everything and you have extra money, these are just some things you can spend your extra gold on. Gives you a little boost in AP, Health, and the ability to see wards and invisible players.

Most people go into the defense tree because Kat is a squishy character, but this is how I see it. If the enemy wants to focus you down, having 4% less damage taken and a little bit more dodge will NOT save you from dying. However, having a shorter flash cooldown, some extra runspeed, shorter cooldowns (Shunpo away from trouble), and some good judgement WILL save you. Also this lets you get the extra experience, a faster and longer ghost, longer neutral buffs, and less time dead.

First of all, you are going to want to grab middle. Kat gets much much stronger when she levels quickly because all of your abilities start to tie together and your runes start to kick in.

Early Game:
Always throw a Bouncing Blade to help your jungler when the game starts, and then go to the middle and start last-hitting creeps with your Bouncing Blade. Getting the last hit is important enough where you should risk getting hit by a few melee's or spell's, but don't overdo it. You are going to need this gold from the last hits if you want to pull ahead. I dont even try to harass until around level 5 because you simply dont have the damage and survivability to do so against competent opponents.

The objective here is to stay in your lane long enough to get 1900 gold, so you can go get your Hextech Revolver and Ionian Boots of Lucidity at the same time. This is about the same time you should start looking for people to gank.

What I like to do is be very proactive about ganking. This means asking your teamates if they are struggling with a certain hero, checking the top and bottom lanes for heroes below 50% health, and asking your jungler to cover your lane while you gank. This stops your middle lane from getting pushed, gives your jungler a little xp boost, and allows you to snipe some enemy heroes.

Mid Game:
Once you get some ganks, and start building up your items, you should be entering the part of the game where you and your team need to stick together and push lanes, kill dragon, and get neutral creep buffs. Sticking with you team is going to be where you shine as Kat.

What you want to try to do is before teamfights, activate Preparation and try to bait them in with a few Bouncing Blades. By now you should be at least level 13, and you will have maxed out Bouncing Blade and Shunpo. At all levels, Preparation gives your Bouncing Blade full damage no matter how many times it bounces, making it insanely good for pre-fight harass.

Once the fight actually begins you are going to want to wait for the enemy team to use a few of their stuns/silences before actually going in. The beauty of Kat is that all of her damage can happen in about 4 seconds, so even if you wait for your teamates to get around 50% health, you can jump in and kill the entire enemy team before you lose allies.

Late Game:
If the game has gotten to this point, it means you are either god status or do nothing status. Hopefully it is god status and the enemy team is just being stubborn. The hardest part when this happens is to not get cocky. Even though you can probably destroy their entire team in 4 seconds, by now they have caught on to what you are doing and will put every single stun/silence/supression they have on you. But don't panic, USE IT TO YOUR ADVANTAGE! If you stay back and harass with your Preparation + Bouncing Blade, they will be so worried about you coming in and destroying them that they won't use their skills on your teamates, allowing them free-reign to plow their way through the enemy base with you sitting just behind them scaring away your enemies.

Well this is it for my guide! Try it out and tell me what you think. Feel free to post stuff in the comments about anything you think is missing, needs a change, or just comments in general. Thanks a lot, hope this is helpful to some people. :D