I'm not going to give an in depth guide on how to play karma like a certain 100 page top rated guide (http://www.mobafire.com/league-of-legends/build/the-comprehensive-karma-72191?page=1#chapter10), But I am going to correct a misconception. That being that a bot lane support who farms is a terrible bot lane support. Bot lane supports do not farm and thusly buy gp5 items for thier gold. As a gp10 bot lane support, karma does terrible. Virtually any otehr option for her is better. Note that all ALL tiem builds EVERYWHERE are to be changed on a game by game basis if the need arises... only terrible players build the same way every game. This means as an ap carry don't be afraid to buy a negatron first item against that leblanc mid. Buy abyss early if you need mr but not so much that a BV is required... buy VS early if they stack mr, buy zhonyas early if getting focused too hard in fights, and FH first if ad is fed and your team doesn't already have 1.
Pros: Major support utility when played as an ap carry, similar to zilean.
Ability to deny last hits, which is ****ing amazing.
Good sustain thorughout laning phase.
Stupid fast farming mid-late game.
Cons: People will try to deny you mid/top because they don't know how to play karma.
That's the only major con I can think of. Her escape is just ok, but not awful.
Slightly lower single target damage than some similar single target ap carries (brand)
but only because on how hard it is to get full damage from w.
READ: Situational Building
This is one of the most important concepts in the game, and not many people seem to understand.. It goes much deeper than "they have 5 ad so we better all build thornmail" (a terrible idea). Using that example i'll tlak about thornmail first. The only way thornmail is effective is if you have massive amounts of health so that they don't take only 2-5 hits of reflected damage before you die, or if you are rammus or galio because it stacks so well with their taunts. Lets assume they do have 5 ad. Your team would fare much better if you had say a frozen heart on the AP carry or bruiser, a randoons on the support or jungle, a GA on your ad carry, and maybe a thornmail on your tank. The passive& active on FH and randoons benefit your team in fights much more than thornmails. The same goes for other item classes.
Will of the Ancients: This item is so so strong on karma. It's even stronger if you stack the passive with a teammate. (Yes they do stack if 2 people on a team have one but only for those two people.) Encrourage your second ap to build one early too, or if you don't have 2 ap, encourage your support. 50% spell vamp is so good and I can't stress how good it is to have two.
AP carry karma
Karma is a pretty damn fun ap carry... endgame e shields for 1k with a 1k aoe damage while q does about 600 with a healing option. That said to be effective in any way, karma needs solo lane farm... Take top or mid or don't pick her.
AP bruiser karma
Typically a top lane build, karma can build ap bruiser, as is suggested by (http://www.mobafire.com/league-of-legends/build/the-comprehensive-karma-72191?page=1#chapter10)'s build. Make sure to always counter build your lane first when going bruiser. Ex: gp top? buy an early glacial shroud. Kennan top? buy an early merc treads and/or negatron cloak. This is how you win your lane.heal
Note: the fourth pot is there on purpose... you can 4 pot with boots and usually only miss 0 to 1 cs. You just wait on the pad till you have gold for a fourth (10 secs after minions spawn).
Laning like a boss
Observe your lane early game... If you feel you are dominating, and are building ap, buy 3 dorans lucidity and a deathcap... Need more sustain? buy a revolver early. Building to a situation is key. Also buy items early game according to how much gold you have when you back... 500? buy that second dorans... 400? boots of speed instead.
Generally last hit, and harass with q when you can... reserve mantra e's early game (pre 6 ish) for when going for a kill, running away when you are confident you don't need more health, and when you have blue buff, or if you generally feel you have enough mana regen that you can (rare unless you are runed badly).
ProTip: when you have blue buff, or feel you have a lot of mana regen, you can and should be blocking your opponents last hits with your shield. Its funny as hell to watch them rage and you give yourself a stupid large early game lead.
Late Game Playstyle
As AP carry
Essentially, late game, your job is to do ******ed amounts of damage while protecting the people getting hit. The best way to do this is usually to mantra shield whoever is in the middle of the fight taking the most damage and then q from the max range it is effective at... Typically you will want to have w up on someone who is running through enemies for more damage or on someone who might need to escape quickly. Anyway, dont use mantra with q in team fights unless it is completely necessary as it cripples your ability to do damage.
As a Bruiser
Your goal is to run in first unless there is a better iniator on your team... w whoever you deem apropriate, mantra e, q, and try to hit as many enemies with your beam as you can. Attempt to focus the squishy carries.
For the luls. Its silly, but she's honestly one of the better troll junglers... As long as you dont get counter jungled early and killed, her jungle farm is great and her ganks are at least ok. Wolves (get mid to help for speed) >blue (get leash and bot should help dps for a few seconds) >wraiths>wolves>red>double golems>recall build situationally after the revolver
This guide isn't meant to tell someone new to league how to play karma... it is to correct the silly terrible bot lane support farming karma guide that is currently top rated. If you see anything that needs adding, let me know.