The quest will begin with Amata waking you up to let you know that your father left Vault 101 and Jonas got killed and every member of the vault's security team is looking for you. Amata will let you know that she knows a way to get out of the Vault 101 through the Overseer's Office. Make sure to take the stuff on your desk with you.
After leaving the room, head to the Overseer's Office.
Once you're inside the Overseer's Office, access his terminal and open the secret hatch under his desk. If you fail to hack the terminal, you can head back, kill the Overseer and take the password to unlock the terminal.
Head through the secret hatch to the Vault's door.