Like your tagline says... root password.
Get a list of all the servers and Media Gateways and their IP Addresses. Make sure you have all admin and root passwords, including System Platform (assuming you have Avaya Aura). Which server is the licensing server (WebLM)?
Go through the procedures for creating new stations and voicemail subscribers. The regular stuff should be easy. Then ask what are the one-off, random things that happen. What users have two extensions or two voicemail boxes? How are those administered and tracked? What are the procedures for terminations and removing users?
Do you have IP phones? How are phone backup files administered? Do you have access?
Do you have SIP trunks and Session Manager? How are DIDs converted to stations: In ASM via an Adaptation or in CM via incoming-call-handling? Same with outbound Caller ID: An Adaptation or public-unknown-numbering? How about incoming toll-free numbers?
Do you have specific extension ranges for different departments or functions? What are the DID ranges (212 555 1000 to 1999)?
Will you be responsible for reviewing the billing and working with the carrier? How do you contact the vendors? What are the account numbers and circuit IDs?
What are the Disaster Recovery / Business Continuity plans? How do you fix or who do you call for different issues (Trunk outage, specific server down, Media-Gateway down, etc)? What are the Service Level Agreements (SLA)?
Does the system have auto-attendants? Are the vectors documented? Is the verbiage of the announcements written down? Are Announcements backed up to a server or to the Phone Guy's PC?
Ask your predecessor what items he always meant to fix/implement but never got to. What are some lingering, low-level issues that pop-up fairly regularly? Who are the problem children, such as that one VP of Sales?
These are just a few questions to get you started. There's going to be something... A LOT of somethings... that you won't think about until 3 months down the road. There will be a lot of "why is it programmed like this?" moments and you'll just have to recognize them as differences in style. Vector programs can be frustrating that way when you come into an existing system - Especially when a half-dozen different people programmed various portions. Remember the person coming after you and try to make their life easier by documenting everything.