This guide is going to be a guide to an awesome late game Karthus.

Here are his abilities:

Death defied - passive This passive allowes you to cast spells for 8 seconds after your death

Lay waste Creates a delayed blast at Karthus' cursor position. After 0.5 seconds, deals 40 / 60 / 80 / 100 / 120 (+35% of ability power) magic damage to each nearby enemy, this deals double damage if it hits only a single unit.
cooldown: 1 second cooldown.

Wall of pain Creates a 800 / 900 / 1000 / 1100 / 1200 distance wide wall through target point. Reduces enemy armor and magic resistance by 15 / 20 / 25 / 30 / 35 and reduces movement speed by up to 40 / 50 / 60 / 70 / 80%; debuff lasts 5 seconds. The wall lasts 7 seconds.
cooldown: 22 seconds cooldown.

Defile Toggle Off: When Karthus kills a unit, he restores 20 / 27 / 34 / 41 / 48 mana.
Toggle On: Drains 30 / 42 / 54 / 66 / 78 Mana to deal 30 / 50 / 70 / 90 / 110 (+25% of ability power) damage to nearby enemies each second.
cooldown: 0.5 seconds cooldown after toggeling off.

Requiem - Ultimate After channeling for 3 seconds, Karthus deals 250 / 400 / 550 (+70% of ability power) magic damage to all enemy champions (regardless of distance).
cooldown: 180/150/120 seconds cooldown.

quick tips
when you die you might have the chance to get some kills on your soulstealer. Toggle defile on and spam the **** out of the enemy with lay waste