I just bought this champ and am having difficulties figuring out how to play her. I usually play mid and figured to try her there with no success. And I get dominated on top lane too. Anyone have good suggestions and/or guides?

Basics

R>Q>E>W with one point in each by level 3.

21/9/0 As much AP as possible, health/armor/MR in defense.

Ignite/Flash. Pretty much the only two you should run, anything else is sub-optimal for combo-killing and escaping on Kat, which is all she can do really.

Boots+3 pots
Revolver
Sorc Boots
If owning hard: Gunblade -> Rylai's -> Rabadon's
If struggling: Rylai's -> Gunblade -> Rabadon's
If getting completely eaten alive mid: Abyssal ->Rylai's-Rabadon's
After that, possibly Void Staff, GA, Rabadon's

Kat is a mid lane champ that is almost entirely dependent on match-up. Enemies with skill shots like Xerath, Brand, and Ahri can be defeated, but it's pivotal that you actually dodge their skills. Enemies like Le Blanc, Kassadin, Cassiopeia, Mordekaiser, Ryze, and Veigar will stomp you most of the time.

Kat is only as good as her ult, and any hard cc will almost completely cancel out your damage. This means you either don't play Kat against these sorts of champs, or be extremely patient and wait for them to use their cc. In the case of Mord and Ryze, they're too tanky/healy to really kill while still having large damage output.

Farm up until 6, harass with E+Q if possible, and go in for the combo. Ignite->W->E->R->Q and if they're half health or less they should be dead, unless of course you're cced during R.

Kat is kill dependent, and can snowball hard with enough gold and kills. Shut her down though, and she's negligible for most of the rest of the game.

In team fights, use Q from afar until tank engages. It's important to keep track of your enemies' cc during the fight, only go all in once you're sure most of it has been used. A well timed ult from Kat can be devastating to the enemy squishies, which you should be targeting, and if it lands you a kill or assist will reset your cooldowns. Be ready to use your cooldowns when this happens, it's a waste to not follow up.

Other than that, practice makes perfect. Look for opportunities to shunpo away using your team mates or wards. Much like Lee Sin, you can carry wards with you to place over walls and shunpo to, allowing you to escape.

Good luck!

Check out Tiensinoakuma's guide on mobafire or solomid.

Above info is a decent start. However most serious Kats agree:
No Rylai's.

[Mpen] Boots, Gunblade, Deathcap -> other ap stuff (situational)

Being (I think) the one un-nerfed gold item, I often see Tiensi pick up Kage's Pick in slow games.

Harass is key as Kat, unless you've really snowballed you'll rarely kill anyone straight up 1on1. Harass -> assassinate, or bust into teamfights late and ult -> shunpo kills are your best bets.

Honestly I would watch a pro streamer play her like Scarra. I never understood Kat at all until I watched her played at high elo.

with most champions, people focus on positioning.

with kat, the focus shifts to timing. time your entrance into the teamfight when everyone already has a target. then jump in and create havoc, hopefully before they notice and react.

I've been building Rylai's on Kat forever since it's her only shot at CC outside Gunblade. Why is it such a bad choice on her?

Gunblade provides AD, Spellvamp, Lifesteal, and AP.

Her main harass in lane, her Q, scales better off of AD, but still has AP scaling. By hybridizing this into one item, it becomes the best damage item for Katarina to scale in damage. Not only this, it provides lifesteal and spellvamp, allowing for her Shunpo to heal for about 50-70. This is great in lane, as it's a free ½ of a health pot every few seconds.

Not only this, the active of the gunblade allows her to hold enemies in place. The gunblade is the true reason she can kill AD carries without them simply waltzing off in a different direction. Not only this, 300 damage is quite a bit. Often times it's all I need to finish off enemies. Other times I have to catch up to enemies by using my Shunpo on a ward, then using its active.

Rylai's provides her with health, sure, but that's about it. Her slow on her Q is negligible, and the 35% slow on her Shunpo is moot compared to the active on the Gunblade.
Sustainability is, oftentimes, much better than health, as it provides "virtual" health.

TL;DR
Gunblade has more damage, gains massive sustain, and has a nice proc.

Also, the hell's with the downvotes?