For runes 2 max your damage in late game i get magic per lvl yelows and blues, magic pen marks and for some early damage i take Flat AP quints.

But if you are not confident at your mid safety you can take some flat magic res or per lvl.

I dont take mana regen for simple reason, karthus E skill is your mana sustain.

Exhaust is great for making you Q easy 2 hit but its not the only purpos it have, it lowers damage from spells that your opponet dose so it might help you at trading blows and allso it can save you from many ganks if your wall wont be enough. Flash is ofc for both atack and def, you can go in with flash or go oute, safe you self from gank or death at mid.

You can allso take other spells depending on game, altho leave flash.

Other options :

Ignite - Im not fan of ignite on karthus but if u are laning against some 1 like Swain who heals him self with ulti ofc you can take it.

Teleport - I often take Teleport couse it lets me go off and farm far from my team ( ofc you should have map warded for that so you dont get cought and killed) and if case i see that there is team fight going 2 start soon and i wont make it on time just by walking there i use teleport, allso its great for ganking, asck your team 2 put ward in bush at bot lane you can teleport 2 it for a gank if bot lane will be pushed by your foes.

You goal at mid is not 2 in it but 2 oute farm it and carry your team in late game. Ofc if you can kill the mid its good but thats not your main target in game. Try staying mid untill you are lvl 6 befor going b for first shooping.( but ofc if you are realy low on HP dont do it)

Use your ulti not only for last hiting kills, after you get your ulti watch the map often cheack lanes if some 1 is low on hp or your team m8ts are starting 2 fight if you see them lowering the health in attempt 2 kill use your ulti, if thay see your ulti thay should continue 2 atacking, assists are allso important.

In early you should focus on farming and lasthting creeps, you can use Q sincee your atack animation is rather slow, but try 2 lane Q the way it only last hits the minion you wont and not does damage 2 others minions, you should not push so you wont get ganked. If your mid foe is agresive try 2 hold him off with Qs whan he atempts 2 poke you with his spells.

In mid and late Game consider actink like suicde bomber, go in, turn on E use wall for slow and mr/armor shred, keep landing Qs , and hope your team will folow you, after thay kill you, use Q 2 more times if some 1 is still in range or cast Wall and one Q, dont use Q more than 2 times otherwise you wont mange 2 cast your ulti, after you did casted Q 2 times or Q+Wall, use ulti.

Askc your jungler for giving you blue from ancient golem whan he can, later on just take it you self if you dont have other team m8 that realy needs it.

For starting items there are 2 options. Normaly i start with Sapphire Crystal + 2 potions of Health. But if you are vs some 1 like brand or galio where you will need 2 dodge his skill grab boots and 3 pots.

Your item goal depends on how is game going, if you have some real hard time mid, the guy in mid jsut pushes the lane 24/7 and your jungler aint ganking, you might get tear for mana befor going RoA so you can kill creeps with Q and E and hold the lane. If the guy mid harras you hard and drops you low on health all the time, get Will Of The Ancients, spell vamp should let you stay on lane. Sorcers and RoA is your main item Goal. Start with Catalyst the Protector as soon as possible, it helps in early with each lvl it regens your Health and Mana, saved me many times after trading blows and killing the guy i survied ignite thx 2 lvling up and having this item. Get RoA asap but after Catalyst the Protector grab boots then think what you need more, fnishing RoA or sorcers. If game is going fine after RoA get Death Cap for more damage, then If thay start 2 get some MR, get ether void or abbysal, Get Zhonya's Hourglass if thay got some AD damage that is couseing problems, allso this will help you a lot whan you go in use it right whan thay start 2 focus you or even befro that,if thay got some CC. Get Rylai's Crystal Scepter for slow efect and some more HP.

Allso some times its good 2 buy Mejai's Soulstealer if you know thay dont have champions that will kill you easy early game. Get stacks with ulti, paly safe, less SUICIDE BOMBER TACTIC at last in early. This item works extreamly well on karthus since you can get kills and asits even if thay kill you, this way you can keep stacks high.

This bouild is ment for ranked playing but it works fine in normal games.

PS: Sorry for my bad english.

If you dont have intiator in team , like malphite. amumu or others who opens the figth with his ulti or jsut by going in, you can act as initiator, slow them with wall, flash in and start doing your job, ofc dont do this oute of no where, first ping and write in chat lets fight.