Greater Mark of Insight: These are useful for what else bypassing enemy magic resist.
Greater Seal of Replenishment: I use these because it helps early game with mana but is loses its usefulness later in the game.
Greater Glyph of Potency: I use these to assist in early game kills. I feel that if you dont do well early game you won't do to well later game.
Greater Quintessence of Fortitude: Add a bit of surviability.

The masteries I chose gives Karthas surviablity and can continue to dish out damage

Sorcerer's Shoes: Basic caster shoes
Majia's Soulstealer: If played correctly Karthas ends up getting quite a few kills giving him a lot of stacks
Rod of Ages: Good for survivability and AP
Rabadons Deathcap: usual caster item
Rylai's Crystal Scepter: Good slow for his E spell, surviability, and AP
Void Staff: Good magic pen and more AP

Use lay waste to harass and farm. In a team fight stand by and cast some lay waste once the initial burst is over or you think you can use defile without dieing go for it. Use wall of pain to run, keep people from running, or to weaken the enemy in a team fight. Don't waste requiem. Coordinate with your team to get kills in different lanes or kill enemy champs who have ran and got away with low health. Don't expect to always get the kill as it can easily be countered by item such as Banshee's Veil and abilitys that shield or regenerate health.

Clarity: Great spell for Karthus because he does suffer from man starvation
Flash: useful for escape and chasing
Ghost: useful for escape and chasing
Ignite: early game kills
Exhaust: great for preventing escape but wall of pain is basically the same so it might be a waste
Other summoner spells: I don't feel any of them would be of great use to Karthus

Pro:
Good Farmer
Good Harassment
Can get kills in other lanes
Can continuously dish out damage
Con:
Semi squishy
No definite escape ability
Needs good map awareness
Needs good positioning
Mana Starved

Good champ if played correctly. Don't initiate fights leave that to the tank. Keep on doing damage but try to stay alive. This is my first build so sorry if its not made correctly. Hopefully it helps out. Good luck.