Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
In this guide, I will teach you how to play Katarina in a basic way, so that players new to her will easily learn how to do it, and what to build, in which situation.
I picked the runes so as to still deal alot of damage early game, and the magic penetration because of those few rascals that get those magic resist runes, you can go for full AP runes, or maybe switch out the quintessences for some more magic pen, health runes are good too, but I would not recommend it since Doran's Shield covers it all.
I picked 10/0/20 masteries, so that I could still stay in a lane while dealing damage, the ignite mastery should help you out considering what runes you have. The movespeed mastery helps as well, a little bit of maneuverability always helps.
The build shows the perfect item build, although it may be expensive, you have large amounts of lifesteal and spellvamp, keeping you alive through fights. Grabbing alot of hp and survivability to keep you alive early and late game, while still being a potent threat, and as you can see, the build is leaning more towards the AP, since dps would not benefit shunpo at all, while this buid benefits all abilties.
Flash and ignite are a must, if you wish to, take exhaust, but ignite would help you to get a few early game kills, but on the other hand, exhaust could be used offensively and defensively.
Flash is important, as you can flash and then shunpo to a nearby unit.
Heal is useful, but not recommended, your spellvamp and lifesteal should keep you alive, and this takes room for more important spells.
Cleanse is useful as well, but to be honest you shouldn't be going near any CC anyways, if anybody argues that you will be near it anyways during teamfights, dont, because you should wait until they use their silences and such.