Please be aware that this build is still being tested, changed and refined, so check back regularly. Also, if anyone has any suggestions, tell me!

Currently testing:
Will of the Ancients - could provide lots of spell-vamp ontop of the heal from Heavenly Wave. Might also heal allies if you use them as your Spirit Bond anchor.
Spirit Visage - Worth the cost? Provides MR, CDR and a 20% heal increase. However, the increase to heal is probably better replaced by an AP item which would increase it by more, as well as for allies.

Special thanks to:

• Foggy12 for the awesome banner. Check out his GFX shop.
• Hypershatter for showing that you don't need AP early-game & the self-cast shield trick.
• Shellibix for continual support, and for introducing me to LoL.

Abbreviations

AP - Ability Power.
CDR - Cooldown Reduction.
CC - Crowd Control. Slow, taunt, stun etc.
AOE - Area of Effect.

Shield - Soul Shield.
Bonus - Usually Mantra's bonus effect.
Bong - Spirit Bond.
Wave - Heavenly Wave.
DFG - Deathfire Grasp.

About this build

I don't want this to turn into a huge wall of text, so for the larger paragraphs i'll include a tr;dr at the bottom.
Contained within this guide are 3 different builds:

• Hybrid - Hybrid caster with decent survivability, best played as support.
• Offtank - AP-Offtank caster with large survivability and decent damage output. Can't really be played as full tank as you have no taunt or large CC abilites.
• AP Carry - AP Caster with huge burst damage.
• Support - AP Caster with emphasise on auras and support. Generally only take this if you know you have a good team.

All 3 builds are close to the CDR cap to speed up gaining Mantra points, and lots of AP.

Hybrid

Pros:

• Good support character - shield, heal, slow/haste.
• High survivability for a support.
• Potential high damage output.

Cons:

• CC can be a problem lategame.
• Mana-hungry earlygame if you harass a lot.

Offtank

Pros

• Large survivability
• Good damage for a tank
• Gets better the lower health she has

Cons:

• Has no strong CC - Only slow/haste.
• Useless if silenced or stunned - hence Cleanse.
• Vulnerable to finishing nukes, e.g. Garen's Demacian Justice or Veigar's Primordial Burst.

AP Carry

Pros

• High damage AOE abilities.
• HUGE burst damage on a single champion.
• Can shield and heal yourself - deceptively strong at low health.
• Can hold her own defensively 1v2 using Spirit Bond.

Cons:

• Useless if Silenced. Worth taking Quicksilver Sash or Cleanse if they have a character such as LeBlanc or Kassadin.
• Semi-squishy.
• Gets focused in teamfights. Needs to be paired with a good tank for teamfights, e.g. Shen or Rammus.

Support

Pros

• Can be one of the best support champions in the game - Has heal, haste and shield.
• Support abilities also deal damage.
• Works wonders with a good team

Cons

• With a bad team, you'll get ********ed as you have no real survivability or killing power.
• Again, CC is an issue.

I take Greater Mark of Magic Penetration for all four builds, as there isn't much else to take for these.
For the Hybrid and Support builds I take Greater Seal of Fortitute, Greater Glyph of Cooldown Reduction and Greater Quintessence of Cooldown Reduction. Provides a little survivability along with extra CDR as you want to be able to heal/shield your team as often as possible.
If I'm playing as Offtank I take take Greater Seal of Armor, Greater Glyph of Magic Resist and Greater Quintessence of Scaling Cooldown Reduction.
For the AP Carry build I take runes for utility. Greater Seal of Health to allow for more aggressive harassing early-game, Greater Glyph of Mana so I don't run out of mana harassing and Greater Quintessence of Cooldown Reduction again, for the extra damage output earlygame.

Why do you take CDR/lvl for the Offtank build, and straight CDR for the other two?
I take CDR/lvl because tanks/offtanks really come into their own mid/lategame. By the time teamfights start, the CDR/lvl should outstrip the flat CDR runes. The other two builds, however, rely more on harassment earlygame.

I generally take 9 points in Offensve and 21 in Utility for the extra CDR.
However, for the tank build, I take 21 points in Defense instead - this provides the buffer you need at the start of the game.

Skills-wise, Karma is a unique champion. To be able to play her effectively, you need to remember this. Instead of an Ultimate ability, she has Mantra. It is automatically available when the game starts, and when activated, Karma's next ability has a bonus effect, consuming a Mantra charge. Karma gains a Mantra charge every 30 seconds, up to a maximum of 2 at a time. (Time reduced by CDR.) Using Mantra on the right skill at the right time is essential to play Karma well.
When laning or harassing, I generally keep 1 Mantra charge at all times to shield myself if I need it, and use the other for harassing or healing when it recharges. (Whee Mantra patterns :D)

is your passive ability. It provides extra AP the lower health you are. (Around 1 AP for every 30 health down). Enemies often underestimate this. Basically, the lower health you are, the tougher you are. If they towerdive you when you have low health, you should easily be able to kill them with Soul Shield, Spirit Bond and the active from Zhonya's Hourglass.

is your bread and butter skill with most of these builds. Generally, I used mantra on this for the heal. This means you can lane almost indefinitely as long as you are careful to last hit and keep an eye on your mana. And, with a high amount of AP, the AOE % heal on this is really strong, bordering on overpowered. Lategame this can heak ~10% health to every ally, while at the same time dealing decent damage to your enemies. In team fights positioning this well is essential so that you can hit as many enemies and allies if you used Mantra on it!

is Karma's hardest ability to master. It only deals damage to enemies it passes through, not your target. Basically, you should cast it on whoever is the most mobile in a teamfight. Rammus with Powerball on, Xin Zhao or Miss Fortune. However, you also need to decide whether to boost your allies or slow your enemies. Only experience can really teach how to use this skill. Not really worth using Mantra on, as it just increases the movement speed buff/debuff.
Protip: Using this on an ally so you can get somewhere quicker is always worth the mana.

is our third ability. It's a simple damage absorbing shield in it's normal mode, useful in fights and that's about it. However, when you use Mantra first it deals AOE damage around the target when cast. This is a perfect ability to use Mantra on. Try casting the upgraded Shield on your tank just after he initiates, or an ally who is towerdiving. Used well, Soul Shield can deal high damage with a decent amount of AP, but is best used in teamfights or for defending yourself when you have low health. A nifty trick with this is to bind self-cast E to the T button on your keyboard, so you only have to press a single button to cast shield on yourself, potentially saving precious seconds. [Thanks to Hypershatter.]

Now, the long part...
After all, Karma has sooo many items suited to her needs. The item builds included with this guide are what i've found best for each role, but should be mixed and match depending on your team and your enemies team. The mark of a good player is being able to vary their build and playstyle dependant on circumstance.

Quicksilver Sash is a must for ANY BUILD if their team has lots of CC.

Hybrid

Your core build should follow along these lines:


This gives us a decent amount of AP, enough health to be able to use Karma's passive, Inner Flame to it's full potential, and the active from Zhonya's Hourglass. Said active is indispensable, since you should be staying at pretty low health for a large amount of the game to utilise her passive. Rod of Ages also makes sure we don't run out of Mana.

I generally get the items in exactly the order on the build when I play Karma as hybrid, as early-game there isn't much that should cause you problems. Not if you have a semi-competent team, atleast.
Very rarely will you get beyond those 4 items. If you do, you should finish off Lich Bane from your Sheen as at this point you will have enough AP to make it worth using over Sheen. If the game goes on for absolutely AGES, then the enemy team will probably have some MR. Abyssal Mask's aura is perfect to counter this. Rabadon's Deathcap is just icing on the cape for some serious ***-rape.

Offtank

This build uses Karma's shield and heal to be able to stay in the middle of team-fights for a long time. Remember that you SHOULDN'T be iniating, however - leave that to your tank. Building Karma as a full tank wouldn't work that well since she has no taunt abilities and would be ignored by enemies.

Your core build focuses on gaining armour and magic resistance aswell as a little AP. You don't really need a huge amount of AP to be useful in teamfights - the buffs from your skills do that already. HOWEVER, atleast a little is needed.

Again, this provides the active from Zhonya's Hourglass for those OHSHTSHTSHT moments, as you should still be hovering at around 35% health. Banshee's Veil is also invaluable against CC based characters such as Kennen or Lux.
If you finish those items, Abyssal Mask is again a good choice as it provides magic resistance and AP, then finally a Rylai's Crystal Scepter for the health, AP and the slow. But, again, you probably won't get that far. The reason for getting AP later in the game is because early-game your abilities already have a decent base damage, and your passive gives you free AP anyway. Combined with the CDR of Frozen Heart you should be dealing pretty consistent damage anyway.

AP Caster

This is the build that focuses on dealing damage. I can almost guarantee the majority of players will try to play Karma as a standard AP caster. While Karma is semi-viable like this, she needs a few specific items to excel at dealing burst damage.
Your core item focuses AP, CDR and passives/actives.

Honestly, without Deathfire Grasp, Karma's late-game damage is somewhat lacking. This makes up for it, aswell as taking a HUGE chuck out of anyone you use it on. You should generally use it's active at the start of the fight since it deals 30% of CURRENT health, not max health. Lich Bane provides even more burst damage, by increasing your attack after each ability. With the tiny cooldowns on your abilities, you should be using an ability -> auto attack -> ability -> auto attack combo almost continuously in team fights. 1v1, a single round of your abilities, each followed by an auto-attack should devastate any squishies and deal decent damage to tankier characters. However, our burst damage still isn't amazing, since our AP is still only about 150. This is where you buy Rabadon's Deathcap. A single one will increase the damage of your full combo by ~1.2k. After you have one, just buy any AP items you want. I generally buy more Rabadon's Deathcaps, since they give the highest AP of any single item, but they can, and often should, be replaced. The only shame is that their passive is unique D=. The most likely problems you'll have with this build are that you're getting decimated by their casters such as Ryze, inwhich case take an Abyssal Mask or they are just stacking Magic Resistance, which is countered with Void Staff.

Support

This build is highly situational. Unless you're sure you and your team can pull it off, take another build. If you're tank isn't good, then your carries are gonna get ********ed. Then, you're gonna get ********ed. Think about it.

Your core item should be along these lines:

Yes, you got that right. It's YOUR job to get Oracle's if they have a stealth character, it's YOUR job to buy wards, it's YOUR job to sacrifice yourself if necessary. Don't always expect a positive K/D. Try and aim towards a positive K+A/D instead. This build should be viewed similar to Soraka. Squishy.As.Hell.But.Good.If.Played.Well.With.A.Good.Team. You cannot carry your team to victory. Your job is to be useful, to keep your lane partners health up, shield them, help them escape if necessary. Don't forget that. You shouldn't be alone AT ANY POINT. At any point that you're on your own, you're just walking gold. Other good items for if you get the cash include Banshee's Veil, Will of the Ancients, Elixir of Brilliance or Rabadon's Deathcap.

Well, I really don't want to turn this into a huge wall of text, so...

Hybrid/Support

Pair with a high dps champion such as Tryndamere or Pantheon. Avoid pushing your lane, just keep last hitting. Keep you and your lane partners health up, while harassing your opponents. At some point, you and your team-mate should try and kill them, preferably when they have less than 60% health. Make sure you communicate when. When you do, use Spirit Bond on your team-mate. Tryndamere is a perfect partner as he can slice past them and dmg both with Spirit Bond, as is Tristana or Renekton. They'll probably attack your partner, at which point you use a Mantra enhanced Soul Shield on him, followed by a Mantra enhanced Heavenly Wave. They will probably realise the futility of this, and try to run. If Spirit Bond is out of CD yet, cast that on the lowest health enemy. If not, you can use Exhaust or let them escape.
You should follow a similar pattern throughout the game, sitting back and supporting your team-mates. If you are playing Hybrid, you can be a bit more aggressive mid-late game than normal for a support, but you should still be careful. In teamfights, just spam your skills on the most dangerous targets. Shield-wise, if it comes to a choice between saving yourself and saving a carry, save them. They're more important. Lategame, you should really stay with your team. You will get raped in a matter of seconds by any carry or nuke.
tl;dr: Play safely.

Offtank

If your team has a jungler, you are a perfect char for solo lane. (This stratagy focuses on you being in a solo lane, but you should get the gist even for duo lanes.)
Focus on last hitting and harassing until you have 2 points in Heavenly Wave (Level 5). Once you have level five, keep harassing, but keep an eye open for opportunities. If you want, ask your jungler to come and gank. Either way, until you have atleast Glacial Shroud you should be playing fairly defensively. Don't give your opponents any chance to gank you, as you don't have any amazing escape mechanism. (Although Spirit Bond and Exhaust are OK.)
Once you have your Glacial Shroud and you boots, you should start heading around and ganking as much as possible. If your turret is being pushed, use Fortify and head to gank them. Fortify useful if someone is trying to tower dive you.
Once you gain your Needlessly Large Rod you can start 1v1'ing people, within reason. Don't run up to a Tryndamere who'll just ult on you.
Once you get into team fights, hopefully you'll have your Frozen Heart and maybe Zhonya's Hourglass. You should sit just on the edge of your team in fights. Far enough out that anyone who attempts to attack will get massacred by your ranged carries (You should have one. If you don't have a ranged carry, then you don't need an offtank.), but close enough to spam Heavenly Wave and for the Aura on your Frozen Heart to work.

td;dr: Play defensively until you get Glacial Shroud, then gank. Use Fortify to protect turret. Sit on the edge of teamfights and spam spells.

AP Carry

Even as a carry you should play defensively early. You focus should be on last-hitting for gold and XP. Only harass when you can do it without losing any health. Your focus is on surviving until mid-game and getting enough money for Sheen and Deathfire Grasp. Of course, if enemies are on low health, if you think you can get the kill, go for it.
Once you get those two items, however, you can start raping.
Generally, you want to be 1v1ing other casters, preferably low-damage ones. Don't go and 1v1 Ryze, of course, you'll die. Other support characters and champions such as Janna and Kayle are easy, and you should be careful against nuke casters such as Annie.
Gank as much as possible to gain money. You primary aim should be to gain lots of money, while defending your turret. Fortify is a good way to do this, if you want to use a summoner spell for it, or you can focus on last hitting at your turret.
Once your team starts pushing and getting into teamfights, you should be sitting on the edge with your other casters and ranged carries spamming as many spells as possible, focusing damage spells on their carries, and shielding your carries. This is important. With the huge amount of AP you have, you shield can absorb a lot of damage. This could easily make the difference between your main carry dieing or not. Better yet, use Mantra before casting it to deal a lot of AOE damage around your carry :).
In ANY fight, you should start with the active from Deathfire Grasp and follow it up by spamming Heavenly Wave. For a 1v1, use Mantra on Heavenly Wave, in teamfights Mantra is best used on Soul Shield.
tl;dr: Play carefully. Go for kills if you think you can get it. Don't forget to last hit. Focus on gaining gold and exp early game. Mid-game, gank a lot, aswell as killing the idiots who try to push a side turret on their own. Don't forget to use the active from Deathfire Grasp.

In conclusion:

• Play sae
• Last hit
• Protect your carries
• Position yourself well
• HAVE FUN

I hope this guide has helped you, atleast a little. I hope you actually read it, as it did turn out to be rather a big wall of text. Sorry about that. Anyway, I hope it helps you :)
I currently only have around 25 games with Karma, so any suggestions, alternative stratagies and tips would be great :)
Have fun playing Karma :)
She really is a unique character.

Since Karma is an especially complicated champion, videos are a particular effective way of showing how to play her. Just take a look at how they play.
http://www.mobafire.com/league-of-legends/forum/videos-and-streams/an-ap-nuke-karma-match-my-youtube-2098
http://www.youtube.com/watch?v=7JDOejgyzls


If any of you guys don't like free advertisement, let me know, i'll take it out :)