After your character has perma-died, you will be brought back to the log-in screen where you will have to log-in again. Upon logging in you will be back at the Character creation screen where you will have to make a new character to be able to continue playing Face of Mankind.
Perma-death is, like the name says, permanent. So make sure you always got enough Clones.
Perma-dieing is also the only way to change your character's appearance (beside clothes) or name. However, when you make a new character you will start again like any other new character: no items, no rank, and the default starting money. You will have to build up everything from scratch again.