Hey! My name is BeastlyNinja9 and I am a Katarina main. I used to main support (Blitz, Thresh, Sona) but found Katarina and climbed decently high with her for a silver player, peaking at Silver I 100 LP before I lost 3 in a row and demoted to Bronze on a major tilting spree. Fun stuff. And yes, I said Silver I. This isn't a guide for all you Plat/Diamond players, this is for those hardstuck bronze/silver players (which is pretty much 2/3 of all LoL players). I eventually changed my name to Kataclysm (with a capital i instead of an L) at the end of Season 7 because of my love for the champion. I find it very fun to play this champion and she never gets boring. Let's move along, shall we?

In my opinion, Katarina is always a really strong assassin if you know what you're doing. If you don't, well, let's just say you won't have a great time. But you're here to learn? So why Katarina? I personally think Katarina is extremely bursty and it's amazing to see the amount of damage you can deal in a teamfight. If you ever look at the damage charts, you'll almost always be first or second in your team (and usually even the game) because of your one-shotting in teamfights. Katarina is a great champion in lower elo and even in higher elo. It's more rewarding in lower elo because people don't seem to know how to play against Katarina because she is a pretty rare champion in low elo. They tend to walk near her daggers to let you dish out a ton of damage on them and even get a ton of kills in a teamfight, as seen below. In higher elos when they're smarter, you can still use dagger positioning to get a great engage in a teamfight. She's also extremely mobile for a teamfighter, not even considering her burst. If you learn how to play Katarina, you will never face limits on this champion. She doesn't have limits in terms of mastery, similar to other common champions like Riven or Yasuo, unlike champions like Annie who don't have nearly high of a skill cap. There's always room to learn on Katarina.

Katarina Quad

Pros

Lots of burst damage
Good in teamfights
Can easily fix mistakes you make
Easy to 2v1 with
Snowballs very well, especially with Dark Seal

Cons

Hard to learn
Mechanically difficult
Requires quick reaction
Not very tanky
Hard to play during late game

PRIMARY (Domination)

I personally take Domination primary with Electrocute, Sudden Impact, Eyeball Collection, and Ravenous Hunter. Sudden Impact is self-explanatory. Eyeball Collection tends to be the better option over Zombie Ward since it benefits you with damage instead of extra vision by destroying wards. Ghost Poro is horrible on Katarina because she is always moving and never stays in a bush long enough for it to summon.

SECONDARY (Precision)

I take Triumph because of how good it is on Katarina and it supplements more whenever she gets a kill, along with her resets. It saves her from any last laughs from Ignite or towers and it saves your life a lot when you dive under tower. I take Coup de Grace with Triumph since it helps you assassinate the low targets in the backline or it helps your ult damage since Death Lotus is one of the last abilities in most of your comboes, so they'll be low to die to it.

Voracity:

"Whenever an enemy champion dies that Katarina has damaged in the last 3 seconds, her ability cooldowns are reduced by 15 seconds.

If Katarina picks up a Dagger, she uses it to slash through all nearby enemies, dealing magic damage."

This passive is the reason why Katarina is commonly called the "Reset Queen". 15 seconds is greater than the cooldown of all of your basic abilities and 15 seconds off of your ult. This means you can use your combo to one-shot the adc with ult, use it again on their midlaner, then use your combo onto their support, use your combo on their squishy jungler, then use combo on their toplaner and use ult to kill them. My point is that you can get 2 ults off in one fight during midgame. As for the dagger pickups, they deal an immense amount of damage with the right items and still are strong even with the nerfs.

Bouncing Blade:

"Katarina throws a Dagger, dealing 75/105/135/165/195 (+30% Ability Power) magic damage to the target and 2 nearby enemies. The dagger then ricochets onto the ground behind the primary target.The dagger always lands 350 units on the opposite side from where it struck the first target, getting there in the same amount of time regardless of how many times it bounces."

This is Katarina's main ability that helps her farm or poke or use at the end of the trade. When farming with it, make the most out of it by waiting for the 3 melee minions to be in range of killing for your Bouncing Blade.

Preparation:

"Katarina tosses a Dagger into the air and gains 50/60/70/80/90% decaying movement speed over 1.25 seconds."

This is Katarina's ability for utility and helps defend herself when an enemy ganks by simply pressing the W button. This along with her E can be very useful when chasing or being chased.

Shunpo:

"Katarina dashes in the blink of an eye to the target ally, enemy, or Dagger. If it is an enemy, Katarina strikes for 15/30/45/60/75 (+50% Attack Damage) (+25% Ability Power) magic damage - otherwise she strikes the nearest enemy in range. Picking up a Dagger will reduce Shunpo's cooldown by about 80%. Katarina can blink to any location near the target."

This is Katarina's bread and butter. This is what makes Katarina the champion that she is. This ability can be used for jumping onto someone, jumping away from someone, or just to get to an area faster. Used with her Daggers, you can dish out a ton of damage with your passive, Voracity.

Death Lotus:

"Katarina becomes a flurry of blades, rapidly throwing knives at the three nearest enemy champions, dealing 25/37.5/50 (+22% bonus Attack Damage) (+19% Ability Power) magic damage per knife.
Total over 2.5 seconds to each enemy: 300% bonus Attack Damage (+0) (+0) magic damage. Applies Grievous Wounds to all enemies struck, reducing their healing and regeneration by 40%."

Yeah, this is it. Katarina's Death Lotus. The "wtf is that cooldown", the "seriously that damage tho", the "report our midlaner", the Coup de Grace in it's pure form. With Gunblade, you'll be unstoppable (assuming you're not super behind). This thing does crazy damage if you use it at the right time, and since it also gives them grievous wounds, they have no way to survive this. Comboed with your E, you can get in the middle of 3 people and ult and do a hell of a lot of damage. However, if you get CC'd by most hard cc (excluding snares/roots since you don't need to move), it gets canceled and you're in the middle of 3 people defenseless. This just makes Soraka a big pain in the butt when you're teamfighting. Due to your passive resets, you can actually use this twice in a fight if you combo well enough, as seen below.
Play Video

The moment you've all been waiting for! Now, we will go over the combos of Katarina, when to use them, and what they are good for. Remember:

D = Dagger ( Voracity Passive)
Q = Bouncing Blade
W = Preparation
E = Shunpo
R = Death Lotus
AA = Basic Attack/Auto Attack

Level 2 Combo

Q -> E(immediately after Q)-> AA -> D-> AA-> either (E (on enemy -> AA)) or (E (away to a minion)

This combo is when you just hit level 2. You want the level advantage on them, so you'll have to pull this off as soon as you can after you hit level 2. The second you hit level 2, do Shift+E (or whatever hotkey you have to level up abilities), then pull off the combo. This best goes with the element of surprise, so remember that! You hit level 2 on the second wave first minion. A way to be even more surprising is to use Q to finish off the last minion and level up E as the dagger hits the enemy then finish the combo.

Level 3 Combo

E -> AA -> W -> AA -> D -> AA -> Q -> AA -> E -> AA -> D -> AA -> Ignite (optional) -> E (away)

This combo seems super hard, but it looks a lot tougher to pull off than it seems. Pretty much, after every dagger/ability casted, you auto attack to get as much damage off as possible. The reason there is an AA -> E -> AA is because Shunpo resets your AA timer. All you really need to remember is E-W-Q-D-E-D-E which STILL sounds hard, but trust me, it'll be easier when you're in the game.

Level 3 Combo (with Gunblade)

E -> AA -> W -> AA -> Gunblade -> AA -> D -> AA -> Q -> AA -> E -> AA -> D -> AA -> Ignite (optional) -> E (away)

This is pretty much the same as the first combo, but with an extra Gunblade + Auto. It may not seem much different, but Gunblade impacts your combo greatly. The Gunblade itself deals 175-250 damage and plus 80/90 with the auto, but that's not why it impacts it so much. The gunblade has a 40% slow for 2 seconds, meaning that it's almost impossible for them to dodge your dagger pickup after you use it.

Teamfight Combo

E -> W -> Gunblade (carry/squishy target) -> R -> D -> Q -> E -> AA -> D -> AA

You may notice their aren't nearly as many autos, because in teamfights, those 3 seconds can save your life and ace their entire team. If you did autos between each thing, you would probably get demolished because their team already CC'd you either before you ulted or right after you ulted. The reason why Q-E-W isn't as good in this case is because Bouncing Blade is at a short range and it makes you have to move forward to use your Shunpo. You don't want to be too close to their frontline since if they have someone like an Alistar, they can knock you away or engage on you like a Leona could. Also, doing E -> W lets you blink over any skillshots like an Ahri's Charm coming at you whereas it's almost impossible with Q -> E.

Core Items

Hextech Gunblade

This is Katarina's core item. This synergizes very well with her kit and helps her stay alive in teamfights while shredding everyone else. The active helps a LOT with assassinating squishies or anyone in general. The mix of AD/AP is also very good on Katarina, whose abilities scale both AD and AP. The AD also changes adaptive damage (e.g Electrocute to physical damage which is useful if your enemy laner is building MR against you.

Zhonya's Hourglass

This is Katarina's second core item. You usually do not get this first item as it delays your power spike by quite a bit, so you shouldn't. If you ever feel like you need it, such as facing a Zed or Talon, still don't. Just get the 2 Cloth Armors from it and then get an item from Gunblade. If that still doesn't satisfy you, turn it into a Seeker's Armguard. If their Zed is pooping on you with 4 kills at 5 minutes, take a Stopwatch and that's all you'll need.

Situational Items

Morellonomicon

This used to be a terrible item on Katarina since she had no mana, so she had no way of inflicting Grievous Wounds efficiently in teamfights. Now, it has swapped places with Liandry's and replaced the old burn (which wasn't that good on Katarina in the first place) with Grievous Wounds, which you'll need against healing midlaners. Unless everyone BUT your midlaner doesn't heal (such as Vladimir top, Warwick Jungle, Soraka Support and some **** like a Volibear ADC you shouldn't get it VS. the enemy team.

Liandry's Torment & Rylai's Crystal Scepter

The only reason I didn't do these separately is that these items are terrible without each other on Katarina. Most people think "Why would new Liandry's be good it has no magic pen and burn is useless on assassin!11!!!" But look. It says in combat. That's about 5 seconds in combat. If you set up a dagger with Q, it'll charge up Liandry's passive for when you engage. You take this with Rylai's because of its double burn damage. Rylai's is pretty bad alone on Katarina because you already have the mobility to chase people down, so don't get it alone without Liandry's.

Mejai's Soulstealer

You only get this if you're really fed and don't have many deaths. A good way to check is if you multiply deaths by 4, it'll be less than your kills. You should have at least a 4:1 KD ratio otherwise you can't abuse this as hard. If you do, great! You can get up to 145 AP and +10% Movement Speed. This means if you have 4 items (Gunblade, Zhonyas, Rabadon's, Mejai's), you'll have 581 AP! If you have Void Staff, you'll have 680 AP, not even including the Magic Penetration you'll have with Void Staff + Sorc Shoes! But if you want even more AP, you can substitute your Sorc Shoes with a Spellbinder and you will barely feel the difference in movement speed due to the +10% bonus!

Spellbinder

I personally dislike this item on Katarina. If you like it though, you should get it. I think that the movement speed passive and active isn't very rewarding on a champion like Katarina since she's already mobile enough. The AP bonus is pretty good, but I don't feel like it's easy to use in teamfights correctly. If you use it at the wrong time, you can possibly lose the game because you didn't use it correctly whereas a Rabadon's Deathcap or Void Staff is more reliable and has more room for mistakes in fights.