Not Updated For Current Season
This is an ability power based build, obviously. I generally go 10-0-2 or 12-1-5 with this build. Your kill sequence should look alot like this: Bouncing Blade -> Killer Instincts -> Shenpu -> Death Lotus. This order should be change if fighting champions with crazy HP regen or heals, such as Taric, Vladamire, or Soraka. If you are worried about their regen or heals. simply use your Killer Instincts first, then Bouncing Blade, then Shenpu and Ult.
Be sure that your team is buying wards. This is very important!
Your first items should be the Boots of Speed, a health potion, and a sight ward. Mobility is the single most useful stat in early game. It gives you everything you need to dodge skill shots, chase down low hp enemies, and a means of escape. The health potion is standard early game health recovery. The sight ward, used with Teleport, however is a very useful part of filling Katarina's role, assassin. Place the sight ward in brush before recalling, teleport back to it, then gank and get an easy 2-4 stacks on your meiji's.
Early game: 0-15 minutes
It is not necessary for Katarina to recall before she reaches about 2000g. This will ensure you dont miss out on valuable experience and money. Warning! Play it safe until lvl 6! You are squishy! Kite your opponents and score last minion hits with a well timed Bouncing Blade.
Mid game: 15-30 minutes
At this point you should already have your Abyssal Scepter and 330 gold saved. At your next recall, sell your Sorcerer's boots and pick up Boots of Swiftness. These boots will ensure noone can get away from you. After the Boots of Swiftness, be sure to pick up the Sheen or if you have the gold, the Lich Bane. Generally the game should'nt last past 30 minutes; however, they sometimes do.
Late Game: 31- god knows when
Your game as Katarina should never go this long! The further along the game goes, your advantage is steadily decreasing. At this point you should be fairly close to completing your build. If not, get the Rylai's Crystal Scepter ASAP! At this point you should always stay away from groups. At 20 stacks on you meiji, some with try and focus you. Play it safe let tank initiate in group fights then shenpu in and wreak havok.