Just buy your items and go to mid lane,or what ever lane you go to, always make sure you help your jungler look for invade and leech for your jungler so you can have a better chance on getting second blue. In order to last hit with karthus be sure to just try to hit one minon with q and not mutiple minons.

Ah heres the fun part as long as you have your seraph's embrace and zhonya's hourglass be the tank your team doesn't need. Go straight in making sure you have your defile(E) active zhonya's to make your self alive longer and use seraph's embrace too, when you die you can ulty depending on if the enemy team are low health.

Pretty the same as Mid Game except it will be harder for you to stay alive.

Flash
Exhaust those two summoners will help the most honestly because since you have your ult you wont need ignite to finish off your job
you can also take teleport instead exhaust

Oh yeah in rank games dont go like a yolo monster in Mid Game and Late Game because it can hurt your team in the end