Level 1:
At this point Kata is generally super weak, and will get poked/zoned by any champ. The goal here is to avoid taking damage. Q farm for minions, give up CS if necessary.

Level 2-3:
Here you can noramlly go for a quick trade or even a kill depending on the matchup. If you are against a champ that can't match your level 2 (think veigar, syndra etc), with dblade conqueror, you can kill level 2. With other matcups that can match your level 2-3, go for an electrocute trade (always small repeated trades in this case). You can also look for skirmishes with your team/jungler at this point in the game. Kata is really strong in skrimishes, play around your reset passive. Remeber small trades repeated, can set up a solo kill, or a gank for your jungler. The mini game is generally to always take winning trades.

Level 6:
At this point onwards Kata is strong enough for really strong roams/decent trading, especially if you have recalled before this point, or even picked up a few early kills. From this point you can really snowball your lead.

If Ahead
Create numbers advantages, play around objectives, look to really set opponents behind and get your team ahead. Pick up turret plates and team fight.

If even
Just side lane, and join your team when a fight/objective timer is happening. Look to build an advantage from farm/picks/objectives.

If behind
Minimise your mistakes from this point, try to get turret bounties/shutdown gold, pick up what farm/turret plates you can, give objectives if necessary and wait for a mistake from the enemy.

At this point Kata is very glass cannon, if you misplay in a team fight you can easily get killed. You really want to focus on finding perfect openings in team fights. Generally Kata falls off late game into most comps.