These answers are somewhat accurate, if you are playing public games, or pre-made with friends.
There is no static build to any champion.
That being said, I somewhat disagree with the builds being posted in the answers, if you are wanting to play katarina in SoloQ, sorry guys :(. The Katarina they are suggesting is glass cannon, and is fine if you aren't playing solo-queue, but I promise you, going full mPen or full AP, you will die. Alot. You will get CC'ed once, and that will be the end of you :)
Unfortunately, super-anti-fun season 3 is a little bit different in higher Elo. Katarina is a very niche pick, usually used to counter Melee sustain tops like Cho'Gath and Garen. She generally starts 11 pots 1 ward, or 9 pots 2 wards. I would rarely start boots 3 with Katarina, as you have one of the best gap closers/escapes in the game with shunpo.
First B should be L1 boots, and Giant's belt, and the rest in pots/wards.
Go back to lane, and work on finishing sunfire cape+haunting Guise if Vs. AD in lane, or go Warmogs if vs AP. (i tend to skip sunfires and rush warmogs). After that, it's somewhat situational, but basic core items are Sorc shoes, sunfire cape, warmogs, Liandrys, abyssal, and the 6th would be a toss up between DFG, Rabadons, Void Staff, Zhonya's or Guardians Angel.
One thing to note, if you go into the math and theorycrafting of "most effecient use of gold", Katarina actually has reaaaaally bad AP ratio's on her skills since her latest nerfs, about 4-5 months ago. Ratios to the tune of .45 on Q (first target), .25 on W (!!!!!!!), .4 on E and a whopping .2 on her Ult.(per knife, mind you, but it's still really low)
I don't know how long you've been playing LoL, but those AP ratios are garbage compared to what they used to be, and do not warrant building full AP, and is basic proof that Riot does not want Katarina as a snowballing APC. Her base damages are alright, which actually makes it a better use of your gold getting mPen and Health.
Edit: forgot to actually answer your quesiton, 9/21/0, mPen reds, armor or scaling HP yellows, scaling MR blues, AP or movespeed quints or flat HP quints.