Most players often look over the potential of an AD Katarina build. If you look at all the other builds most are AP centered, with very little AD. Though most will not consider AD for Kat it is a viable option. He ratios play a large part in this:
Bouncing Blade: 30%-AP/80%-AD
Killer Instincts: N/A
Death Lotus: 25%-AP/50%-AD
So how does a AD build benefit this? Several ways. Not only will your Bouncing Blade do loads of damage, your ultimate will scale faster than if you built AP making it much easier to shred champs. An AD build makes Katarina a better mid game champ, since most AP builds take a while to get going. Along with this it will allow you to farm easier, making you Bouncing Blade do tons of damage. And you will have a decent auto-attack, not that on Katarina it does much.
Voracity - Passive
Katarina's passive reduces her cool downs by 15 seconds after every kill/assist. Since her 3 base abilities have less than a 15 second cool down this means they are instantly refreshed. So if you land a kill and need to either get out/ kill another person, remember Shunpo will be back up so you can either jump away or onto the next victim.
This is Katarina's most versatile skills. If built correctly you'll be able to clear minion waves as quickly as some casters. This is something that is lost in AP builds since it isn't scaled as quickly by AP. This also gives Katarina a great harass, much better than Shunpo. Shunpo puts you behind the target, making it difficult to get back in position and often resulting in you taking a greater amount of damage dealt or possibly in death. With Bouncing Blade you can hit your target and even get a few minion kills. Another technique for harassment is to hit a minion with Bouncing Blade and hope it hits the enemy champion. This allows you to focus on farming while harassing at the same time. This can also be used as a kill. Say the enemy champ is low on health and is trying to defend their tower or they are running away. Try using Bouncing Blade to hit the champ by hitting it of minions first. With a little bit of luck you'll get the kill and leave the other champion wondering what just happened. It's a good laugh too.
Killer Instincts gives flavor, versatility, and depth to Katarina's abilities and strategy. When activated, the next ability you use has a unique buff on it, as listed:
Bouncing Blade: Each dagger does equal amount of damage; reduces healing to the target
Shunpo: Reduces damage taken for 3 seconds
Note: Her ultimate is not affected by Killer Instincts
Killer Instincts must be used carefully. At lower levels it has a very long cool down and often you don't want to be stuck with out it. Combined with Bouncing Blade it can be used to clear minion waves quicker, or as a harass by bouncing it off minions into champs. When clearing minion waves try to use your Bouncing Blade first, and then use it combined with Killer Instincts. Try to always wait before using Bouncing Blade so that you'll get the maximum amount of last hits.
When using Shumpo you nearly always want to pair it with Killer Instincts. If you're using it for anything other than last hitting a minion you want to use it. If you're going to kill/poke/gank an enemy champ you must have it activated. If they other champ decides to attack you, you want to be able to take it long enough so that you can kill them. Even if you are certain you can kill them it's good to have it activated since you will still take less damage. Katarina is incredibly squish so you must ration her health carefully. If you are low on health you will most likely be killed if jumped on. If you're jumping into a team fight be sure to have it activated because you will be focused. Katarina does damage thus you are going to be focus and the less damage you take the more you can dish out. Always be careful with your health.
Note that when you activate Killer Instincts it's a huge tell. Katarina's blades light up and glow. Once players see that they know something is going to go down. To prevent this try one or both of two things. 1) Try to activate Killer Instincts long before you use it. This way you are more predictable what you will use it. 2) Use Killer Instincts immediately before your next ability. A way to use this tell to your advantage is to activate Killer Instincts to fake to the enemy that you're about to do something, keeping them at bay and not letting them get farm.
In most AP builds this is the main ability, though in this build it does relatively little damage. The best use for it is to get from point A to B. This is useful when jumping on a champion or getting away since it can target friendly units. Also note that it can target wards and most traps, such as Teemo's mushrooms, or Shaco's jack-in-the-boxes (But not Caitlyn's traps). Used correctly though this ability can be devastating, even in an AD build. If you have an enemy champ low on health under the tower Shunpo can be used to jump on them (possibly killing them and if not, then you can kill them with other matters), and then after you land the kill the cool down will be refreshed and you can jump out. This allows Katarina to be a great tower diver, even with her low health. If you're chasing an enemy champ it is great to catch up to them. Even if you can't reach them, you may be able to reach a minion and jump to them landing the kill with you Bouncing Blade.
Finally, Shunpo gives Katarina versatility. Try to save it (especially early game) to dodge abilities. If you can, dodge burst shots (such as Ashe's volley or Grave's gun spray) by jumping behind the champ and (if possible) sinking in a kill. It's also great to dodge long range ultimates (like Ashe's, Ezreal's, and Lux's).
Katarina's Ultimate can shred enemy chapmions. If you can use it correctly you can get numerous kills easily. She throws 10 daggers over a period of time at 3 different champions. In team fights this will shred three of their champions. In 1v1's or 1v2's this will hurt them quickly. The greatest counter to Katarina though is Crowd Control. Avoid attacking champions who have stuns/fears/suppresses etc. If you do attack a champion with Crowd Control jump on them and wait for them to use their ability and then activate your ultimate. If your ultimate is interrupted you are fairly worthless and might as well just run, if you can. Note that Katarina's ult can see through stealth. If you watch carefully you will be able to see when it lights up that an enemy champ is in range, and if you can't see them then they're likely stealthed. It also will attack champions in the bush so even if they run into the bush do not interrupt your ultimate they will still take damage and most players do not realize this. Along with this, when facing Akali do not fear jumping into her smoke circle and using your ultimate, either she will die or she'll have to run out.
Laning for Katarina is fairly open. Playing Katarina mid, especially with this build, can help boost your exp gain so you hit your mid game peak quicker. It also gives many opportunities to gank along with Katarina being able to escape ganks quickly with Shunpo. I would suggest midding, but if you need to lane you need a viable lane partner. The best lane partner has one thing: A stun. If you can find a lane partner with good stuns then you can really dominate the lanes. Specifically Leona compliments Katarina perfectly with a host of stuns as well as plenty of health and a great initiate. Ashe is another good partner since she has long range, slows, and a stun. If there isn't another champ with a stun go for range, and if you can't get that then the tank. Do not try to lane with a AD auto-attack champ. It will not work.
As there is champs that will compliment Katarina there are also champs that make a good counter to her. Never lane againt Fiddlesticks, it will not end well. Though do not fear casters in mid lane. Often this will be perfect since they often don't have much health and Katarina can do considerable damage. Also make sure to keep a close eye on their mana bar. If you notice it is low then strike, they won't be able to do anything about it.
The order of items that you buy during early game is based entirely how well you are doing. As written, the order assumes that your are doing decently, about a 1:1 K/D ratio. If you are doing well, say 3-0 K/D then go for the second B.F. Sword before the Rylai's. And if you're doing really well, say 5-0 early game, consider even getting one or both B.F. Swords before your Sorcerer Boots, but be aware that you will be much slower. In the late game the items you buy is based on the other team. The Hexdrinker is a good item to get since it absorbs a lot of magic damage. If there is a considerable amount of crowd control, consider getting a banshee's veil instead. Even though the mana boost is a waste for Kat, the spell shield with hopefully protect you from any interruptions to your ultimate. Finally, the guardian angel is good since, as Kat, you will be focused a lot. Not only does this help you not die, it will mess the other team up since they have to kill you twice, allowing for your other team members to get them low enough for you to kill. If there is a lot of attack damage a Zhonya's Hour Glass gives a healthy amount of armor with its active, a 2 second temporal stasis. This will be beneficial in later team fights.
If used correctly, Teleport and Heal on Katarina can be devastating. Katarina is incredibly squish and most other people know this, and try to exploit it. Having heal gives you a nice edge and can surprise the enemy champ. If they go in for the kill because you're low on health, immediately jump behind them and attack, when you're low heal and finish them off. Very fun and you'll get a good laugh.
Again used correctly teleport can give you that early game edge. If you're one of the lanes is in a battle and the other team is low, teleport in and take the double kill, though try to avoid kill stealing. This is also a good late game spell for tower defending/ back dooring.
The biggest mistake you can make during a team fight as Katarina is trying to initiate. Katarina can get into team fights quickly with Shunpo, but do it prematurely and your team won't be able to get into there quick enough to support you and you will die. Wait for your team to initiate and jump in a little bit after it's started and a little bit before they start running, or your team does. Make sure to use any abilities on items that you may have such as the Zhonya's active, or Banshee's Veil's spell shield, or the Guardian Angle Revive. If you're almost dead in a team fight do not pull up. Chances are you will not get away since Katarina isn't the quickest at getting out. Your best chance of surviving is to land a kill and be able to Shunpo out, with Killer Instincts activated. Also, remember that Katarina is a great chaser with her abilities so If they're going to get away with no health keep on their heals. Similarly if you're running away with no health and being chased by someone with equally no health don't hesitate too much to turn around, jump on them, and kill them. Also great for a good laugh.
Early to Late Game
Under this build Katarina is quite dynamic. She thrives the most mid game, being able to dish out loads of damage. Though early and late game she suffers a bit.
Early Game - During early game Katarina is incredibly squishy. During this time try and focus entirely on farming by getting last hits with your Bouncing Blade. When you get Shunpo in most cases it's not a good idea to use it as a last hit for minions since it will put you out of position risking the possibility of the other champion taking some of your precious health. The best way to last hit with Shunpo is to move up field putting yourself out of position first and then using Shunpo to get back in position. If you have a significant more health than the other champion then use Shunpo as a poke and possibly a killing initiate, though make sure to have Killer Instincts activated. As a defensive tactic, since you will not have flash, consider buying a ward and placing it near your tower so you can get away quickly without need to have a minion nearby. As an offensive tactic, place a ward in one of the bushes and teleport to it to get a gank.
Mid Game- This, I consider for Katrina, is after she gets her ult and before team fights become the norm. During this time you need to work the hardest, since this is when under this build she thrives. This means many things: Kill the champs in your lane, gank as much as possible, do not neglect your farm. Your farm is incredibly important. This happens with many Katarina players, they focus too much on killing and end up getting under-leveled and an under-leveled Katarina is a dead Katarina. If you can get your items quickly you will be able to continue to level quicker and get more items quicker allowing you to stay viable late game.
Late Game- This is when Katarina under this build falls down a bit, and where Katarina under an AP build thrives. This is why mid game is vital for this build to continue to work. If you are able to be better than the other champs throughout mid game then you should continue into late game and still be better. The two most important things late game are: Do not initiate (See the chapter on Team Fights) and do not go off alone. Just play it safe and continue to get kills.