As far as I know, only gate agents can handle standby requests.

You can stand by on any earlier flight on the same day as your flight.

A List Preferred standbys have priority over regular A listers. Those who get on the standby list early have priority over those who come later. I believe (but cannot prove) that non-rev passengers (airline employees, etc.) have the lowest priority.

When there are more than one A List Preferred passenger seeking standby, it appears that the earlier person has higher priority (but I am not 100% sure of this).

My experience is based on about 30 or so standbys that I have done since the new policy took effect.

A few more standby facts:

I am an A list preferred passenger and travel with my wife, who is on a companion pass. When we both standby for an earlier flight, sometimes the gate agent will clear her onto the flight along with me, even though her standby priority is lower than others who are not successful obtaining a boarding pass. This is done with a wink and a nod. Sometimes, however, I must yield my standby priority since my companion is not allowed to board a flight without me.