Karma is a very unique champion because she starts out with her ult, mantra, which allows her to buff her next skill which is extremely helpful. This also means that level 6 doesnt really mean much haha

I would recommend Flash and Heal over almost anything else for a few reasons. A if your in the bushes and you want to quickly damage someone low on health you can flash out, use mantra+ shield and your Q and do massive damage, but if you just ran you wouldnt be able to do your shield damage most likely. I use shield for the majority of my builds, and I think it suites Karma well because she has insane survivability with her manta'd Q and then her shield of course. Other viable options are Clarity for increased mana and exhaust for a lot of slowdown. Other spells really wouldnt be of much help to you but they could benefit your team such as clairvoyance but i would still recommend heal and flash, because flash can help you escape quite easily as well.

This is the core item build that I use but there is always room to change it up depending upon how the game is going. If you need more Magic resist i would recommend a Banshees vial. Another Item i often use and get earlier in the game if im going for massive cooldown reduction is soulshroud. If you ever feel like you need more health you can build the frozen heart which finishes off soulshroud. The more AP you have the stronger your attacks are as well as your heals and shields so more AP can be just as beneficial as more health, but its all up to how the game is going.
other alternates If your not doing too well in the game then dont get the Mejai because it wont help you very much at all but if your dominating during the early game get it before Rabadons Deathcap so you can get some solid ability stacks

Skill sequence is pretty basic. I would recommend maxing out Q fairly fast because it is extremely helpful from damage and real but if you feel like you need more defense, especially if your playing against champions who have one strong ranged attack, it can be helpful to get more more shield points before your Q. Dont worry about maxing out your spirit bond before like level 13 because even though it is helpful its not going to make a whole lot of difference before big team fights mid/late game.

Early game - Farm minions using mainly your auto attack unless multiple are low on health in which case you can Q to take them all out. Save your skills to harass and kill the enemies cause you'll want most of your mana. Dont overexert yourself early game because you often wont have your W yet and/or it wont be very powerful.
Mid game - At this time you should be able to farm minions extremely easily. Simply Q them to start then walk into the middle and do your mantra+shield to take them all out. Getting up in levels can be quite helpful but since you have solid support skills make sure to help out in big team fights. If your looking to gank an enemy champion and you have 2 Manta's ready and full health I would recommend using mantra+bond and mantra+shield because you wont need to heal if you have full health. In between fights make sure to heal your allies and play smart
Late Game - By this time you should be pretty powerful and have some nice cooldowns. A great idea is to get the Blue buff because not only will you never run out of Mana while having it but your cooldowns will be even further decreased. You should be able to survive pretty well by using your sheild and mantra+Q and since your cooldowns are so short your Mantra recharges quite quickly

OTHER INFO Make sure you support your teammates at all times...if your teammate is coming in for a gank then speed him up with spirit bond or slow down the enemy being ganked. If you are farther away from a target enemy then you can still use your mantra+shield on a teammate close to him/her and not only will it shield your ally but will damage the enemy as well and if that kills you still get the kill not your ally. Your Q also has a very big range, it might not seem that big but in actuality its a little farther than it really says so dont be worried to use it if they just walked out of its 'range'. Late in the game your cooldowns should be extremely short, especially if you have the blue buff so make sure to heal allies in between fights as much as you can. Remember that if your allies run through a spirit bond on an enemy they get a speed boost as well and vice versa. if 2 enemies are chasing you, spirit bond the one farther back if you can because the one closer up will be slowed as well when it runs into the bond.