I haven't really invested any time in her since before she was reworked a while back--I took a long break from video games in general--but I'm familiar with both the champion and the position you're in and I might have some advice that could help. On any given champion--in order to do really well--you need to be familiar with the strengths and weaknesses they have, what portion of the game do the peak in strength (late-game? early-game? somewhere in between?), and what their intended role is.
is an assassin. She does a ton of burst damage and is tuned toward executing squishy champions. Since she scales so well with Ability Power, she generally opts out of high defence in favor of magic penetration and items that steroid her burst damage (


, though the ideal build will vary every game). As a laner, she doesn't have a whole lot to work with, and uses her Q as a crutch against most of the folks she's matched up with--Champions who could otherwise safely harass her with their strong pokes, like 


. However--once she gets a few of those aforementioned items up, she could rip through any one of those dudes thanks to her powerful skill rotation, and could survive bursts of their own with strategically-bought HP+AP items and proper maneuvering--made greatly-easier thanks to her high mobility. On the flip side, she is fairly weak without her ultimate (which hinders her early game), and is quite risky to go in guns-blazing (proverbially speaking, if you like guns then play a marksman) in the lategame when those intense teamfights start to happen (which impacts her late game negatively).
Looking at that, it is important to piece together--in order to be successful with her--that she is a midgame champion. Katarina, like many other assassin's who don't have the stats early on to cut through enemy champions, are tuned toward the midgame. They carefully control the lane by last-hitting with their auto attacks to keep the waves to their side, or shove it with their skills when they start dying to your tower too often. They get as much gold as they can for the midgame--sometimes getting lucky enough to lock in a few kills thanks to a well placed jungle gank--and use that gold to get those cool AP items as quickly as possible. They make decisions like "Hey, should I use my gap-closing skill to jump on Teemo or should I use it to escape that Hecarim gank?". Once they become built, the answer to that question tends to, more often, be Kill Teemo once your burst damage creeps up and your skill rotation becomes stronger in proportion to what you want to kill. Finally: since you would melt from several sources of damage otherwise, one needs to wait patiently for a good opportunity to unleash their burst damage when the enemy team starts to group--especially on Katarina, whose interuptable Ult is thwarted by even the simplest of Stuns.
League of Legends is like playing a s***load of rock-paper-scissors rounds at the same time. You gotta think about how earlygame-champs beat the tar out of midgame champs in lane, but can't do a damn thing against that champion who scales so well into the later stages of a match. You also gotta thnk about how smart it is to stack a bunch of health to deal with all that burst damage when there's this chick who does %HP damage every few quick ranged-AA's and is wearing
; and maybe getting your earlygame-oriented buddy could give you a hand and screw her lanephase up to delay her getting built up.
So my advice is to learn about these different rock-paper-scissors scenarios on the champ you want to do well with, what snowballing is, keep in mind what you should be doing/when should you be buying what/when to level which skills, and especially what items do what so that you can make the most appropriate buying-choices and not set yourself back. Using the most popular build on Mobafire isn't always the smartest move, even if they are helpful, and it's just as important to hit up the League of Legends champion spotlight--or even experienced streamers--to get familiar with the game's/a champion's mechanics.