Your base, core items need to be Always Crystal Scepter and Hextech Gunblade for better survival. Also u can take sorcerer's shoes except from Ionian Boots and Hour Glass For mor magick pen and bigger def. If u doing well u can take Sejais Soulstealer early or Abyssal Scepter, Guardian Angel except from Deathfire Grasp

All runes and masteries on AP at 1st levels for more dmg and easy farm. U can take Magick Pen runes and AP combining them.

MAx masteries for more AP and def, health. Def and health masteries can be combined with same runes for more survivability

Max Q and W early for more damage and. I prefer max q first than W and after 13-14 level max E skill. And dont forget to max your ulti at 6>11>16 :)

Flash for easy gang, initate and for survivability. Exhaust for more ganging and for low damage taken in this combo of Flash and Exhaust its easy to gang kill and initiate. You can take ignite for more damage, but your ulti already hawe it. Except Flash u can take Ghost or Heal, E skill works like flash but if u dont hawe champ or something where u can jump its a problem.

Pros>
Easy gang.
Deadly combos.
PASSIVE <3
No mana makes from you really deadly weapon.
Easy farm .
Nice tits ^^ :D

Cons>
Pretty squishy at jungle.
If being focused die fast.

If u jungle for Katarina, u can gang easy with Flash and E skill combo to get closer to your enemies. At start katarina is wery squishy in jungle so take masteries and runes on armor.

In my opinion best in Katarina is her combos like E>R Q>E>W>R. Great initiator ability and good at team fights. Easy to get double kill with Passive.
Quadra for katarina my max now :D

Spam your Q and W skill, easy to chase minions down.