Sorry for my english, its not very good.
Im not a High elo player, and you will not own wif this build. I'm just showing how I play Karma as an AP support. It's working great for me, I don't get kills, but I do help my team to keep pushing an triunf over the team fights.

I start picking Meki Pendant cause it turn Tears of Gods later and mana regen is all you need at the start. I go first for Tear, cause you will spam skills, since the beggining till the end of the game, and maxing the stacks is just ok... ROD gives you some nice AP, and more health, wat's just great. After having ROD ready, and Tears , just go for the cooldown reduction boots and Rabadon's, then finish up the Archangel Staff.

From now on, the itens are acording to the game.
being hunted? go for Banshee's Veil and Soul Shroude. Great Health, CD reduction.
Want some aura to suport? Soul Shouroud and Aegis.

Want to be more annoying? MORE AP... your shield is a pain in the *** for then when you have high AP... not to tell about the heal.

You WONT have lots of kills. you have to undestand that your roling as a support. your job is to make your team more annoying.

Farm up and haras wif Q, if you get hit, just heal up. Don't waste your mantra stacks.
soon you will be able to kill an entire wave wif R + E + Q .

In team fights your job is simple.. stay behind, use W on champs that need to get closer to do something. you can use it to help nunu positioning to ult, or a xin to engage, or someone to flee.

When the battle starts, harras wif Q, see whos the champ on your team taking the most dmg. R+E on him, and R+Q to heal up. speed up allies chasing, or slow down fleeing or chasing enemys... DONT BE ON THE MIDDLE OF THE FIGHT. it will often kill you, spam shield and Q. but you have to keep one eye on whom to shield.

The more AP ou have, the more your shield will endure. IT'S NOT WASTE ON HER BEING AP.
If your being targeted, save your shield for when your health is low.. it will last longer since your ap will be higher duo to her passive. E + R + Q, W on someone and RUN FOR YOUR LIFE.
when on towers, see whatch minion hes atacking, and shield him. it will give you more time to have the tower.... at higher lvls, 1 shield = 3, 4 hits of the tower... its a lot of extra time for u.

Didn't puted runes, cause I just don't have it yet... like I said, I'm not a high elo... just showing up how I play her..

I'm not a pro, just showing up what worked to me, and I have no complains from my team to me when using her.
Karma fails at nuking.... but shes an incredible support, use that. you wont kill by yourself, but you will be loved by your team.
Exhaust is a really necessary. It saved me many times from certain death, as long as flash too. being Karma, you have to play smart, or you will die.

Note: IF your team sux, you won't be able to do NOTHING... you cant suport a team wen you don't have one.