Hey I'm PerturbdPineappl and this is my first guide. I have had lots of good experiences with Katarina lately and want to share my build

I don't know quite how this works so I am just going to list them without the fancy stuff.

Pros

Insane damage when fed
Resets
Can carry team fights easily
Ward jumps
Amazing roam


Cons

If you lose too bad early you are almost useless
CC is your hard counter
Lame joke
Squishy when built like this

I always max my Q first because it allows you to do lots of poke damage in lane, also it scales better then your W if you can proc the mark. Next you max W because that ill do lots of aoe damage when maxed, and gives you a nice move speed boost for trying to escape. Lastly max your e because you won't really need it other then for you dashes. Always max your R when it is available

Flat AP runes for your Blues and Yellows give you a nice amount of AP, Magic Penetration Reds give you extra damage, and the scaling CDR Quints will give you max CDR at full build, and help with your poke potential as you will be able to spam your Q more and more.

Standard Masteries for no mana AP champs

Unless you are losing lane you always want to get Mejai's. Because of Katarina's ability to roam you can get quick stacks in bot lane which will allow you to do even more damage. If you are losing just pick up a Haunting Guise for the early HP and Magic Penetration. After you finish your Mejai's get a Deathcap so that the Mejai's stacks scale really well. After this depending on how your doing get a Zhonya if you feel you need to survive more, or a Void Staff if you just want more damage. Keep in mind that a Zhonya will give you more damage with its hefty 120 bonus AP, but Void Staff gives Magic Penetration. Always get the Void staff they are getting Magic Resist. After these two items sell your Haunting Guise and get a Death Fire Grasp which will help you 100 to 0 the enemy tanks quicker. When you are at full build you will Insta Kill any squishy that gets near, just beware of any hard CC

Just poke with your q and farm as well as you can. Use your Q to farm if you can't hit the enemy with it. Once you get lvl 3, you are going to want to poke them down with q till they are half HP, and when they are at half HP, use your full QEW combo. After doing that twice they will either be forced to back or will be dead. Remember to use ignite.

As soon as you hit lvl 6 you want to roam. If you don't have your Mejai's yet, wait until you get it to roam as it is very beneficial for when you are roaming. You could go top or bot but I recommend bot because there are two people which means more stacks for you. If your team's lane is pushed, and the enemy is at around half HP, enter through the tri-brush and dive them with all three people. If they are pushed, you can enter through the river but always be wary of wards. Have your bot lane initiate and after the enemy has committed go in on the person with least HP with your QEWR combo. As soon as they are dead jump to the next person if possible. Roaming to top is the same principle just with more tanky people. Roam as much as possible to get those stacks and finish your Deathcap. If executed correctly you will be unstoppable

Late game you should be almost finished with your build and should be inspiring fear into the hearts of the enemy. If you see a squishy alone immediately jump on him/her with QEWR combo and that should delete them. If it doesn't just wait for your Shunpo to come up, and use your warding trinket to ward jump to close the gap, and throw your Q at them for the kill. Don't chase too much or else you might get ambushed. While TeamFighting, you are generally not gonna want to initiate. Preferably you go in last after the enemy team as burned all their hard cc. Throw your Q and Shunpo to the nearest squishy or low HP champ and unleash your combo. Get resets and continue killing people. If and only if you are ultra fed and the team doesn't have hard CC. Don't be afraid to initiate 1v3 or 1v4. They won't expect it so you will have the upper hand. Q 1 of them then E then W then R. Let your R run until it kills at least one person then if everyone else is at Half HP, you can cancel your ultimate by using another ability, and QEW the nearest person. Rinse Lather Repeat. All three or four should be dead in a couple of seconds.