Well for popular demand i am making an AD build for kat. Yes i use it now and then, yes it's ALRIGHT, but AP blows it out of the water. I will use the one played by Dimitrija but remixed a bit. *dimitrija now uses my build :)*
ATTACK vs. AP *READ BEFORE READING BUILD DONT GIVE ME THUMBS DOWN*
Attack Bonuses: Your ranged damage is increased because your thrown dagger does more damage. Also, your hits slow, but your skills dont. The damage output is less then AP
AP: DEFINITELY, WITHOUT a DOUBT better than attack, but takes more skill to be played. On ap you can slow on every skill, your shunpo is a 800 DMG nuke, and your ulti drops enemies/slows like nothing. Also, AP gives your more health and more of an ability of saving yourself *zonya's ring*. Don't give me thumbs down because this is not an AP build.
MY AP BUILD CAN BE FOUND HERE http://www.mobafire.com/league-of-legends/build/katarina-shunpo-that-705
Exhaust: Slows people down for your ult.. ESPECIALLY necessary when you dont have the rylais from AP build. Also helps you dominate and out-damage DPS and get double kills which you wouldnt be able to (shunpo to the further target and exhaust the one that WAS closer to you)
Ignite: Helps you get that essential first kill then finish certain enemies off who just BARELY got out of your ult. Dagger used to be a great tool for this too EARLY game but got nerfed. Now dagger isn't as potent so you should still keep on the ignite train. A good alternative would be flash so that you have some sort of chasing/escape mechanism.
So, for your first item in this situation now, you want to pick up boots of speed firstand 3 health potions
With attack builds, and actually even the AP build. Laning does work well nowadays, even though i still prefer solo.
The next item you want to rush is the Sword of the Occult
Katarina's ability to use shunpo for early kills, in a combination with her dagger, makes her a very versatile early game nuker. You will stack this up pretty fast. Try leveling either your shunpo and bouncing blades to 5 by level 9. The fact is, the base damage on bouncing blades isn't all that much anymore, it is more worth your time to maximize shunpo, even IF shunpo doesn't scale off of AD. The burst will be worth it. Also, now that you can go hybrid, i may start recommending a rylais as opposed to a frozen mallet ;) it is definitely an option and always consider it! Rylais is SUCH a key item on katarina. If you choose to go rylais i would take a rylais after your second BF sword. :) really packs a punch.
Next, you want to turn your boots into sorcerer's shoes.
*PEOPLE PEOPLE. you will say, WHY sorcerer's shoes?! well. your ultimate is magic damage hell, all of your skills are damage, even if you go attack, so naturally, you want the penetration on your ultimate, end of story :) this was mine AND dimitrija's counter to the first nerf she got (you couldnt really counter the 2-3rd one).*
Great! Now you should have 4-5 kills with hopefully little or no deaths and heading into mid game
Mid game is all about rushing BF Swords, you have space for 4 of them, get a phage firstthen 3 B.F. Swords. Turn 1 sword into an infinity edge*you want the chance to crit on the autoattack after the shunpo*
then go for two bloodthirsters to stack attack
To initiate, you want to wait for your tank to go in, however your tank chooses to. When your tank goes in, your offtank or melee will usually follow. RIGHT when they try to hit your tank, shunpo to the one furthest back out of all of them and pop your ultimate. This will leave them slowed while going to your tank and stranded to come back to you. The other thing you can do is wait for their dps to come into sight, shunpo to the dps and ulti only the DPS down, which basically wins you the teamfight.
I would also suggest to stay map-aware, no matter where you are. Mainly because any type of CC can mess with your game, severely. Note which heroes on their team have CC, if they all do, well it might be worth your time to pick up a quicksilver and merc treads :). Keep note of what range their CC is and where they are positioned. Trust me, if you can ulti just out of their CC range, the 3-4 hits from your ult that they take is game-changing.
Hopefully this helped you all :)
I still feel as though AP is better, especially after this patch, but do what you feel like guys :)
Good Luck and Happy Gaming