Katarina is an easy champion to play. Even begginers can use this guide to play. Important think is to use gunblade (most people forgets to use items), cause it slows enemy - Katarina doesn't have any slows, fears or stuns in itself. Katarina tactics is easy - use the killer instinct, shunpo into enemy, throw knive and use ulti. If he won't stun you, he has no chances.
Well, you have when to attack too, and few more things, but its not "how to play" guide but simple Katarina build - good for pro and begginers.

Most items are versatiles, void staff can be changed if enemy team don't have any tank with magic resist (I recommend zhonya or Moonflare Spellblade then). It's also avaible to buy Ionian boots instead of Sorcerer's.

In Katarina flash is'nt as useful as in the others chempions, but it allows u to teleport through the walls (shunpo can do it only with target), flash can be changed for ingite. I do not recommend teleport cause it's useless in mine opinion - I prefer something helping in fight (exhaust) or escape (flash).

This masteries are only an example - it can be changed on thousand of ways.

Many people recommends bounces blades as "leading skill" even in ap build (its nonsense - shunpo takes 75% ap on damage, when blades only 35%), shunpo is much more useful an deadly.

Shunpo is most important skill in Katarina. Its neccesery to remember it can teleport you to enemy and ally. It gives u hundreds of posibilities of ganking, escaping and fighting.

Passive is easy - if u killed an enemy your cooldown are decresed

Well... farming is not a pleasure with Katarina, bouncing blade is only skill with massive damage.

The Pros of Katarina are:
-easy way to play
-powerful ulti
-amazing shunpo
-very useful passive
-nice damages

Cons:
-stun on ulti is your end
-no stuns/slows/fears
-weak farming