When the enemy is low on health behind their tower, consider a Shunpo into Death Lotus combo, as very few champions can withstand the onslaught at critical health. An inexperienced player may not expect the sudden tower dive, though a stun will shut you down quite quickly. Make sure you have enough health to make it out alive.
This strategy can also help you in team fights. If you see an enemy who has low HP, you can Shunpo in, kill them, and then Shunpo out right away. Be mindful of stuns.
A surprise Death Lotus can turn the tide quickly. This is best used in coordination with hard AoEcrowd control, as not having any form of crowd control can leave Katarina vulnerable during Death Lotus. If your team can keep enemies from escaping, Katarina can put out tons of damage.
Remember that many forms of crowd control will interrupt Death Lotus, specifically any stun, silence, taunt, fear, knockup, or knockback. Enemy tanks will save their abilities such as 慎的Shadow Dash or 拉莫斯的Puncturing Taunt specifically to stop you.
Additionally, moving during the cast time of Death Lotuswill also interrupt casting, so once commited to the casting, remain stationary for the full duration.
Try waiting until the other team is already engaged with your team before using Shunpo followed by Death Lotus.
Death Lotus also hits enemy champions which are stealthed. Furthermore, it becomes usable when a stealthed champion approaches Katarina, so keeping an eye on its icon may notify the player of incoming ganks.
Katarina is one of the few manaless champions and is based entirely on cooldowns. Use this to your advantage by using spells whenever possible.
Bouncing Blades makes for an excellent last-hitting spell as it keeps you at a safe distance while allowing for easy farming and doubles as a harassment tool. Try to time the skill to kill as many minions as possible with a single use in order to avoid having the skill on cooldown when other last hits become available. For easy harrass, use it on the minions as they're lined up walking into lane so the last bounce jumps to the enemy champion in the back.
Shunpo and Sinister Steel can be used to quickly and effectively farm minions while directly under your tower, especially at higher levels. Wait for the tower to fire at minions once or twice before jumping in for the last hit.
The first thing to note is that due to Katarina having no mana but relying on abilities is that certain ability power items are less efficient.
In addition, due to her cooldowns, having some cooldown reduction is a good idea, whether you get it from runes, masteries, or items. Try building an early Kage's Lucky Pick and save it to build a Deathfire Grasp, which will help your burst, as let you use your abilities more often.
With the patch V184.108.40.206 (the patch intorducing Elise), the Deathfire Grasp does not grant the cooldown reduction, but is still viable for burst single champion.
Rylai's Crystal Scepter is very useful due to her lack of other forms of crowd control. The 35% slow (counts as a single-target spell for items) on Death Lotus makes it harder for enemy champions to leave her range before she's finished.
Sorcerer's Shoes is therefore the preferred choice of boots, regardless of whether you're doing an attack damage or ability power build.
Sinister Steel and Death Lotus scale from both ability power and attack damage, making hybrid builds effective. However, remember that her base damage and attack speed are not as good as those of other hybrid champions and scale less on level.
Note however, that building a few attack damage items will make you less reliant on your abilities, allowing you to still do damage if you get silenced or are waiting for cooldown.
Hextech Gunblade is a core item of any hybrid build, as it provides large amounts of both attack damage and ability power. In addition, it gives significant regeneration power and a crowd control ability. However, due to its cost, rushing a Hextech Gunblade leaves you much squishier early game.
Lich Bane can greatly increase your autoattack damage output as well as give you increased movement speed for greater mobility.
Even though some of them scale with attack damage, all of Katarina abilities do magic damage. They can always be countered with magic resistance, regardless of whether she's doing an attack damage or ability power build.
Moving away from a minion wave when she throws Bouncing Blades can help you dodge it.
Katarina is one of the few assassins to have a bad laning phase, she cannot heal, has only 1 ranged spell to harass with and is extremely squishy, instead she shares a similar power curve to Poppy, her late game being extremely powerful as her ultimate is a powerful onslaught which will decimate three of your teammembers if not stopped. Prevent her from reaching late game!