There were some complaints on LoLWikia that no one was building Banshee's Veil and Rylai's Crystal Scepter, so I figured I may as well do that. Here you are.

Ok. Seems like a pretty strong character to me, will have to try PvP soon.

Kage's Lucky Pick is so-so, but as a first item, it will pay for itself and the early game is going to be rough in any case.

Haunting Guise seems like a natural choice, it being one of the few AP items for non-mana users, and it being helpful all around, especially together with Sorcerer's Shoes.

Hextech Revolver lets you avoid recalling too much. HP5 runes pick up some slack, especially when you can't afford to get in the fight.

W+E+R is pretty deadly. If they CC you, it won't work, hence Banshee's Veil. If you aren't CCed, Exhaust and Rylai's Crystal Scepter make it easier to get more Death Lotus hits in (unless they have a dash or Flash saved).

Rabadon's Deathcap needs no explanation.

Hextech Revolver can be upgraded to Hextech Revolver eventually if you'd like, but it would have to be a long game and you might as well pick up Will of the Ancients instead if it's late-game and that's how much cash you have. If it's going to be a long game, then Hextech Gunblade + elixirs is naturally the way to go here. I'm just trying to give a main build that matches a more ordinary game.

Shunpo in, Flash out

Well, that's how I like to do it. Depends, I guess. Of course it's better to use Shunpo for both if it's not too dangerous, but what happens happens. You might kill them and not need an escape route, anyway.
p.s. - Bouncing Blade if you need to pop a veil or two.

Finish, don't start

Figure out what you're capable of. Jump in when you can either finish them off, or you can do a hefty chunk of damage and not get killed in the exchange. That's how assassins work, and if your team doesn't want Katarina KSing them, then they don't get how your passive works, how assassins work, or how LoL works.

Don't ult if they can interrupt you

This can be tricky to work around. There's always stun, silence, knockback, whatever. If your enemy is playing smart, they'll try to CC you. But your team also has CC, hopefully, so with any luck, your tank will buy you a second or two to Shunpo into a Death Lotus. It doesn't take long to nuke the better part of an enemy team's combined health, so have at it.

Pros:
More practical to land ultimate

Cons:
Not the most extreme glass cannon ever*

* - If your team is stunlocking the enemy team already, then you could do more damage with a true glass cannon build... but if it's that trivial to ult them, you probably have the game in the bag in any case