1. Speech check Vance to give you the password (requires at least 13%, which is 1 charisma and 27 speech)
2. Talk to Ian, who suggests to talk to Justin. Talk to him, suggest he needs an outside voice, and then Speech check to get the password
3. Get the Black Widow/Ladykiller perk and seduce Karl/Brianna to give you the password
4. Kill Vance and steal the password
5. Although not an actual method, just hack the damn terminal.
These will net you the password (except #5, which is just a way to get in).