Early game you are so powerful because of your passive. Be as aggresive as you possibly can.
At level 2 you can now tower dive with ease. Run in with your teammate, use mantra and then shield him in range of hurting the enemy. Then use mantra again and heal your teammate while dealing a lot of damage to the enemies in range.

As Karma, mid game you will still want to be aggressive, just now keep a teammate nearby. I have found it easier to maneuver and kill if there is someone you can use spirit bond on.
When you get into a fight open with mantra E and then regular Q. Your Q has a low cooldown so if you need the heal you can just mantra heal within 5 seconds.
If you need to escape or slow someone, escape by spirit bond and on the enemy if they are a chaser, but if it is just a ranged use spirit bond on a teammate if there is one nearby. If you are in desperate need of getting away or chasing quickly, use mantra with spirit bond to get a nice boost.

Late game you should try to keep control of blue buff. Use your usual opener but try to stay in the middle of your team, you are not a tank.
If you are low on health use shield and spirit bond and run. But if it is a slow melee, use spirit bond, and then mantra E. Then use mantra Q. Late game you will have around a 12 second cooldown on mantra, so keep kiting him. Mantra E then bond then Mantra Q. Do that over and over.

Karma is a goddess among teamfights. Run in with your team and shield the weakest person, or shield the focused one. Use mantra E if they are being attacked. Use mantra Q as they start attacking, and make sure to hit as much of your enemy and your team as possible. After you do that, you will want to slow any melees, or anyone who is running. Just keep mantra Q on CD as long as you can. If you can use it, use it to your most advantage.