I was playing Karma one day and realized that giving her alot of health and armor could make her a good support with alot of survivability, however she didn't do alot of damage. That's when I thought 'Karma has an AP based shield, and a heal...', and so I built AP like mad. By the end game my AP was 1107, heavenly wave dealing close to 1000 damage, healing 30% of max life, and Soul Shield shielding over 1000 damage, and with mantra dealing over 1000.

This area is fairly self-explanatory. Magic pen reds will allow you to deal more damage against magic resistance. Armor yellows means being able to survive more physical attacks making it easier to fight physical damage champs early game. Finally AP blues, and quints allow a little more damage and shielding early game from Heavenly Wave and Soul Shield.
The reds in this build are pretty standard, however yellows and blues could be changed. If you don't think you need armor the yellows replacing them with mana or mana regen could help seeing as Karma really eats mana early in the game. As for blues and quints you can change them out for CDR, mana, and mana regen to help with the high cooldown of karma's spels and her usage of mana.

Points in offence will allow for overall damage as well as CDR and magic pen. The point in Exhaust is not necessary it is only there as a place holder. Finally the points in utility will allow more mana complementing the passive ability of the archangel staves.

buying boots of speed early will give enough speed to run away early, and a goddess tear will give enough mana for you stay in your lane longer. Then buying archangel staves, rabadon's deathcap, and mejai's will give tremendous AP. The staves will allow for ery high mana and AP, the deathcap will raise this higher, and finally the mejai's will supply both AP and CDR. If you are having alot of trouble getting kills and dieing I would recommend changing mejai's for either a frozen heart, or a rylai's scepter.

The skill sequence for Karma depends on where you are laning. If you have a solo lane skill order should be Heavenly Wave, Soul Shield, Soul Bond. Heavenly Wave will allow you to farm minions without the use of mantra, and heal yourself with. Soul Shield lets you shield yourself and take damage without losing life, and finally Soul Bond will give you the ability to both run away and chase.
When laning with another champ try to lane with either a tank or a DPS. Karma has very good support capabilities for physical damage characters, but not so much for mages. The ability order should be Soul Shield, Heavenly Wave, Soul Bond. The shield will allow you to keep your partner alive as well as dealing damage to your opponents. Heavenly Wave lets you heal yourself and your partner, while dealing damage to opponents. Finally, Soul Bond lets you and your partner either run or chase faster.

The summoner spells I have suggested here are merely that, suggestions.
Spells you should use: Teleport - allows you to reach your allies faster on a push
Clarity - mana helps when you eat mana
Heal - always useful, always.
Smite - Karma can be a very effective jungler, so this can be useful
Flash - basically a "get out of fail free" card
Spells not to use: Revive - no, just no
Ghost - not a bad spell but soul bond does the same thing
Exhaust - again not a bad spell, but soul bond does the same thing
Fortify - if your team needs it they suck defending a turret is easy
Rally - you aren't a tank, you aren't a DPS
Spells you could use: Ignite - useful, but not so much for a burst damage mage
Clairvoyance - while it is a useful spell, sight wards are pretty cheap