Katarina is an amazing assasin and when played properly, can easily carry games. My build is slighlty different, for I use some items that aren't popular on other builds. This is my first build ever, so constructive criticism is welcome :)

PROS
+ Incredibly fast farm (Q -> E -> W)
+ One of the best Ultimates in game
+ Great escape (E - Shunpo)
+ Thanks to the Mobility Boots can gank with great succes
+ If played correctly, can easily score PEEENTAAAAAS :D
+ Does not need Blue nor Red buff
CONS
- Quite bad in early game for She has no reliable CC
- Very squishy
- Can be easily countered by champions with good CC such as Kennen
- I can't think of anything else :D

Creeping on Kata is very easy.
After a certain point in game, Kata can easily farm whole lanes with one sequence of Q->E->W.
You start by throwing a Q on the first minion, then You Shunpo onto an unmarked minion, position Yourself so that You can hit all minions with W and its done :)

Thanks to boots of mobility, Kata can creep minions on the other side of the map and still join the team-fight in time. Kata jumps in, when some of the enemy drops to low HP. Her priority is to target the one with least health.
One thing You should remember as Kata player, is that Your Ulti can be stopped very easily. Due to that, You need to use it when the enemy team exhausts its CC.
When You get caught by the enemy team, use shupo to the furthest object You see, even if it is an enemy champion, then use W, for the speed boost it gives when it hits enemy champions.

Runes are quite obvious.
I take flat armor seals, for it gives You much needed DMG reduction when hit by both champions and minions in early game
Then, flat MR Glyphs for the same reason, less DMG taken in early game.
Flat magic penetration marks to suplement the lack of Sorcerer's Shoes
And flat AP quints for obvious reasons :)

In masteries I will only explain why i chose Brute Force in stead of Mental Force .
Mental Force Gives you only 4 AP, which might be a lot in very early game, but is worthless later on. Brute Force on the other hand gives you the little bit of AD, that will help You with last hitting, which is very important on Kata.

Items on Kata are almost entirely based on the situation.
the only MUST on Katarina is the early spell-vamp from the Hextech Revolver.
I chose this item sequence because:
Mobility Boots give me a chance to roam for the kills.
Will of the Ancients cuz i forget to use Hextech Gunblade aswell as in teamfights, You dont get to use auto-atacks and You can Use the active on Gunblade only once which does not help much when You jump in the middle of fight.
Gaurdian Angel gives me some sustain as well as it cn save my life in fights. Remember, when GA takes effect, Your cooldowns will mostly reset, so You can both attack on Shunpo away.
The rest is arbitrary and can be easily changed for anything else.

The only thing You can possibly change in the summoner spells is the Ignite.
I'd say that the only worthwhile substitute to Ignite is the Exhaust for enables You to chase a low HP target.

IN LANE
For farm: Q->E->W
Harras : Q
Strong Harras: Q->E->W / Q->E->R
For The Kill: Q->E->W->R / E->R->W->Q
Team Fights
E->R->...
Depends if You kill or not :D
If Yes:
->Q->E->W->...
If not: You are f**ked... :D

http://imageshack.us/photo/my-images/715/katab.png/
Feel free to post some pictures of Your gameplay :)