Now that you're inside Vault 88, fight your way through some ghous and follow your waypoint indicator to the terminal in the security wing to lift the security lockdown.
Continue to follow the waypoint until you come across the Legendary enemy, Security Chief Anderson. Defeat the Security Chief who has seen better days and loot his body to find the Vault-Tec Control Board on his body.
With the control board in hand, you'll now be able to get the Workshop operational. Head to the Vault-Tech Workshop by way of your waypoint. Install the control board to gain access to the Workshop.
Toggle into Workshop Mode and clear the debris in the hallway the left of the workshop. Speak to the stranger at the other end to complete Better Living Underground and to start A Model Citizen.