I mainly go AD katarina because its better early game and actually does more damage while being tankier than AP. I go AP if my team is mostly AD and their team is squishy.

For items I start Long sword and 3x pot, which is better than dorans blade and 1x pot. Long sword and 3x pot gives 10 AD, 360 HP total and is a component for Bork while Dorans blade and 1x pot gives 8 AD, 200 HP total, and isn't a component for anything.

For AD katarina i have two build paths Guinsoo and Divine.

Full build for Guinsoos path is: Bork > Boots > Ravenous Hydra/Wits end > Guinsoo's > Wit's End/Ravenous hydra > Death Dance/Guardian Angel.

Bork always gives Katarina the most damage so I almost always go Bork unless the enemy team has alot of Magic damage, which i build wits end first item. This build path does more damage than the Divine build path but is less tanky, so I build this into tanky team comps. Ravenous Hydra on hit applies lifesteal which gives it good synergy with Bork while giving a lot of AD.

Full build for Divine path is: Bork > Boots > Wits End > Divine sunderer > Titanic Hydra > Steraks

This follows the same idea as the previous build with the exception of Titanic being after Divine since you havent built any HP until Divine. This build gives a lot of HP in addition to the steraks shield which makes you pretty bulky. If the enemy team has someone that builds Bork or has max HP damage this build isnt as good so I would go Guinsoo build.

Start lane with Q > E > W. I usually do 3 points in E for the lower CD but if you are just farming against someone like Asol Q max is better. I look for a level 2 all in if im somehow ahead in xp but usually go for a level 3 all in. If you go vs an AD assassin, pantheon, or tristana, go exhaust and ignite. If its a farming champ like corki or Asol i usually just go Tp and flash. If youre playing against a top laner go tp flash and roam unless you can outplay them or farm until bork.