Hello, I'm Sookoll, and I've been maining Katarina for very long time. I am lazy, so i Cba post tricks and Pros & cons etc here.

Glyph - Cdr is a friend of Katarina
Mark - SPell penetration is very obvious.
Seal - Dodge for more survivability + 10% speed from Defensive tree.

For Quintesences i have one Hp quint for Less squishiness. 1 Spell penetration quint for more damage of course, And Cdr is just great. But remember, Spell penetration > Cdr on katarina.

Boots for beginning is must. Dorans shield is BS. You need those boots for fast harassing.
jump in, Q , hit, run & repeat. with boots it will go smoother. People think that Dorans shield is needed to get your health back after harassment. In my opinion HEALTH POTIONS = WIN So yea, I Always, always buy atleast 9 health potions after every recall. These are needed to stay in lane. After First blood( Which I always get) I recall, and buy 9 health potions. Trust me , Potions = Fed katarina = Win. I never buy that much potions on any other champions, I'm feeling like Hp potions are made for Katarina, After your hextech complited you Don't need hp potions that much anymore.

I Buy Sorcerer boots, Mejai, Rylai, Hextech & Deathcap. For 6th item I buy one of those 3 items : 1) Banshee���´s Veil, 2) Hextech 3) Lich bane.
Banshees- if they are having a lot of CC
Hextech - More damage on ultimate & Lifesteal
Lich bane - Sick damage, shunpo, hit , and there you go, another kill.

Best rated katarina build has Cdr boots, which are BS. Every single katarina spell does magic damage, so Spell pen boots are must- My build focuses on maximum damage on teamfight, Cdr boots are not that useful in fights.

Reason why I find Offensive tree to be the best , is because in team fight, you jump in once, and Katarina's duty is to do as much damage as possible, Other builds recommend to go Defensive tree, i agree, katarina is squishy, but with good positioning you don't need Defensive tree.
And as a cherry on top of a cake, in offensive tree you can get improved Ignite and Exhaust.

Spells should always be Exhaust and Ignite. nothing else. Katarina has very good escape mechanism, with Shunpo, no need for flash or ghost. Exhaust and Ignite are needed to get Fed in ranked & normal games.

A thing what's been bothering me , is that most of those Katarina builds around Mobafire prefer Q to E . In my opinion E is a lot of better, always been, Even if i was playing AD katarina before the change. E has smaller CD at higher lvl, It does more damage. It has higher nuke damage than Bouncing blade, And you can last hit really easily without training your Q before E . If you dominate your lane in mid, then you can easily last hit with auto attacks + shunpo. Thing is, you won't ever dominate your lane if you're training BB before Shunpo.
Shunpo has 0.75 Ap ratio - BB has 0.35 Ap ratio
Shunpo's CD is Lower than BB's
Shunpo does 240 damage, BB does 200.
Anyways, Shunpo is definitelly better than Bouncing blades. If you really don't believe me, then Add me ingame (Sookoll) and i will prove it.

If you have brains, Then you will be very successful with this build. Please Rate and comment.
I'd add some pictures, but i really have no clue how to. Please let me know in comments.