Characters may be deleted (or "biomassed") within the character selection window, by clicking on the "X" which appears on the right side of the character's name when hovering the mouse cursor over the character. After confirming that the character should be indeed terminated, the character will be greyed out and a 10 hour cooldown starts. During that time, it will still be possible to log into the character, but doing so will cancel the character termination and the process needs to be started over.
After 10 hours have passed, the character deletion can be finalized by clicking the "X" (now red) again. This will remove the character for good. If the character has been a member of a player corporation, all of the characters assets will be inherited by the characters corporation. They will be moved to the "impounded" hangar of the corporation where the items were located. If the character is a member of an NPC corporation, all assets will be lost irrecoverably.
Character terminations are final. While Customer Support may be able to restore a deleted character in exceptional cases, such characters are always restored 'as is', usually just the character and his trained skills with no assets whatsoever. Customer Support will not be able to recover any items lost with the character deletion.