Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
At first level you get Q so you can get some early farm, and then get either E if you feel like you might have an all in fight at level 2, or W otherwise.
Then you max W first, Q second, finally E. Of course you get R when you can.
Your W and R will be your main source of damage.
AD Kat as a teamfighter
AD kat, like her AP counterpart, can be an amazing teamfighter. However, she needs to know when to go in because her damage with Q W and E isn't enough to take out an enemy from full health. If you have your ult you should just go in and ult in order to secure kills. Remember, you can carry, so don't worry about others calling KS on you. It's a team game, there is no KS.
AD Kat as a duelist
Why would you ever play AD Kat rather than AP kat?
Well, she can duel bettr since she can deal autoattacks after her burst is down. Use that to your advantage. If you don't need to shunpo at first, don't. Just burst them down, then autoattack them a few times. If they get too far away, then you use your shunpo to get back to chasing them.
AD Kat as a trickster
Here's another reason to play AD Kat. People don't know how to build against her.
Since she deals both magical and physical damage, it's very hard to itemize defense against an AD Katarina. Even if the enemy stacks armor, you can deal magic damage with your spells. If they build magic resist, then autoattack them.
Here's what you buy in terms of priority.
1. Flat AD. Flat AD will be the most helpful to AD Kat since it helps both her AA and her W and R.
2. Crit. After you have enough flat AD, start getting crit items so you can also crit.
3. CDR. Get some cooldown reduction so you can ult more.
4. Attack speed isn't really necessary most of the time but if you are in a lot of 1v1 fights rather than teamfights you might wanna get it.