This quest can be started after reaching level 20, or by passing by the area around Quincy Quarries. The Pip-Boy will then receive a new radio signal, at any place in the Commonwealth, called the Vault 88 radio broadcast. Tuning in, the radio will direct the player character to find Vault 88, and open its security lockdown.
The entrance to the Vault can be found in the Quincy Quarries, through a door on the lower left side of the area, facing north. There, a small group of raiders are attempting to breach the same door. Clearing them out will allow the player character to contact the source of the broadcast, and enter the Vault.
It is also a reference to the "Avon Calling" campaign used by Avon Products. Representatives, usually attractive younger women or "Avon Ladies", would visit door to door and attempt to sell cosmetics to the lady of the house.