One item is enough to get her snowball rolling in the game. She just needs to play the initial part of the laning phase properly, get that item and then go on a killing spree (with proper usage of her E and Ultimate R).
Even if she is behind on CS, she can easily make it up by roaming around the map and cleaning up kills. She can even perform tower dives with her team if the enemy team lacks CC, or if her teammate is taking the turret aggro.
Her E cooldown reset mechanic allows her to get multiple kills in a very short span. Combined with her W, it can allow her to perform multiple outplays and escape nasty situations.
She is countered heavily by CC, especially the ones which have no cast time. If she doesn’t use her E properly, then she will end up dying a lot due to being CC’d.
She relies on the lack of vision to roam around and acquire kills. If the enemy team sets up proper vision and has enough map awareness, they can easily stop Katarina from getting a lead.
Mispositioning and using her Ultimate R at the wrong time can make her quite an easy target for the enemy. Her Ultimate R roots her in place, so she can be targeted by a CC chain.
0 - 15 min
Play safe in the early game. You need time to come online and if you fall behind, you will struggle to lane and you will delay your first major power spike.
Katarina is a strong roaming champion. If your allies are strong, look to roam frequently to get extra kills and snowball your lead.
Play around Katarina’s Dagger placements. They offer a lot of extra pressure in lane and will often fall in ideal places to go for favourable trades.
15 - 25 min
Look to assassinate targets that are moving around Summoners Rift alone. Katarina is really good at picking people off and taking down squishy targets.
Once your ADC and Support has rotated to the mid lane, look to split push and pick up gold and XP in a side lane.
Look to group with your team once you hit your item spikes. Katarina is a great team fighter thanks to her AOE Ultimate R which will allow you to dish out lots of damage in a fight.
Play around your Zhonyas Hourglass in late game team fights. Avoid fighting unless it’s available to you.
Stay grouped with your team, but avoid engaging straight away. Wait for the right time so your Ultimate R doesn’t get interrupted.
Assassinate and take down key targets in team fights. Your goal is to clean up fights and deal as much damage as you can before falling down.
Katarina's early game is solid, especially after getting all her primary abilities. She can go for frequent burst trades and roam around to get kills.
Her level six is phenomenal and can completely decimate an enemy team having no CC. She will be able to use it to kill enemies with utmost ease, especially during roams.
Her first item component will give her a damage boost. This will be a terrible thing for the enemy laner as they will have to be careful about all the trades Katarina goes for.
Once she gets 2 points in her Ultimate R, she will be able to do a lot of damage to the enemies in a short time. This means that enemy squishies will be in grave danger.
Her first ability will be maxed out at level 9. This will increase her damage and poke in the game, which will make it very hard for her laner to deal with her.
She is outstanding in team fights due to her Ultimate R and Q > E combo. It is over for the enemy team if she manages to get a flank on them.
When Katarina hits level sixteen, she will be mighty due to her Ultimate R. This will help her clean up the game easily.
Katarina deals a lot of damage during the late game due to all her items. Her burst damage can one-shot enemies and carriers alike.
Since it is the late game, the enemies will have many defensive items. This means that Katarina will have a hard time killing them. Playing around vision should help a lot with this.