Starter items

Core items

Offensive items

Defensive items

Situational items

The above build is a full on offensive build.

For your early game, you should focus specifically on farming up until u get at least level 2 Coda Blade, Along with a level 3 Marauder Knife, buying the level 2 coda before getting your level 3 knife is a very good option also, as it gives a higher AD boost and enables you to fight more in your jungle. whilst doing this you can also use your xray to clear out some wards so as to create some pressure on the side of the map you're jungling.
For the most part pre-level 6 ganks are not recommended, unless a lane is over pushing hard, or if a laner has no means to escape (no jumps blinks etc).

Early-Mid Game (Top Side)- You should focus mostly on putting some pressure on the laner, and be ready to either rotate to bot-lane to raider or pressure turret, depending on your team's call. Also do not forget to clear enemy deep wards, so that you cannot be seen rotating or doing relays.

Early-Mid Game (Bot Side) - Focus a lot on getting your levels quick by farming, this will enable you to be more effective in 3v2 or 3v3 fights, however avoid using your ultimate in close combat 3v3s as your damage will drop tremendously. Also clear the raider area of wards regularly.

Mid-Late Game (Top Side) - Focus on keeping your laner from getting ganked, or counter ganking, your ganks will be a lot weaker than a champ with grabs, knock downs and such, all you have is a slow in your QW > E combo. However if your laner gets the enemy low, don't hesitate to commit to secure the kill, ultimate is extremely effective in dives as you don't take turret damage during the ultimate's duration.

Team fights - Never go in first. it is the worst possible move you can make, one should always look for a flanking opportunity on their carries, and trying to single them out off their team. unless following up something like a Wonder Woman prime ultimate or an Atrocitus ultimate, you should never ult a team that's grouped, as your damage will drop substantially and you will reappear in the middle of their team, which is exactly where you don't want to be.

Extreme Cases - If your team is behind, but has a good amount of cc, a great option for katana is to split push a side lane and farm the smaller jungle camps simultaneously, this gives her a huge boost in credits over a short amount of time, and the ability to rejoin team fights stronger than before. However in doing this you need to be careful if someone comes to push you back, check if he or she can fight you, if she can it is best to go back and force a team fight before he can rejoin, as staying will only end up forcing you back eventually and forcing your team into a 4v4.

Perks of Katana - early lifesteal items like Cheetah's Claw or Soultaker Katana, enable you to do early objectives solo, like Doomsday device. Katana can solo this with lv3 Marauder Knife and Lv3 Coda Blade followed by Lv3 Soultaker Katana or Lv3 Cheetah's claw.

Item situations, against cc champs like atomic green lantern or star saphire which can slow you or stun you from range, Mobius Core proves to be a highly effective item, as well as Entropy Aegis.

In the eventuality that a team stacks up armor, Atomic Axe will be a must buy.

And in the extreme case you are forced to split push, high AD items followed by Rip Hunter's time pack will make you very slippery, and enable you to push really fast.

Lobo's Chain is only a buy you should get if you are getting bursted down too quickly or if youre fighting against something that's kiting you a lot, consider modding it with hook shot as well in this case.

I should note that katana is by no means a low level skill cap hero. She is easy to mingle with but Extremely hard to master.

On the other hand she is extremely fun so enjoy playing her to the fullest!!