What is typical ATC procedure when a non-pilot calls from a commercial flight for help?
There is absolutely nothing &quot;typical&quot; about such a situation, which is also why - as is the case for most abnormal situations and emergencies - there are no detailed and specific standard procedures for dealing with it.
Many ATC units around the world have adopted the general &quot;ASSIST&quot; checklist to deal with abnormal situations. This would likely also be the starting point for handling a situation like the one you describe:

Acknowledge: Let the person making the call know that you understand the situation
Separate: Provide extra separation to other traffic around the aircraft in question
Silence: Stop all unnecessary talk on the radio, switch other aircraft to another frequency, to ensure a good line of communication
Inform: Alert colleagues, supervisors, rescue personnel, the airline/flying club, other aircraft in the area etc. as appropriate. Get more people working on coming up with a solution.
Support: Help the passenger/cabin crew in any way possible. Maybe the controller has flying experience, maybe someone who was contacted in the previous step does and can step in and help guide the passenger/cabin crew.
Time: Try to estimate the possible timeline. Is the aircraft literally falling out of the sky, or is it flying along steadily on autopilot? How much fuel is left? Don't force anyone to make rash decisions if not necessary. Time produces good decisions.

But, again, there is no standard procedure, since such a situation could present itself in countless different ways. There are simply too many variables to come up with a &quot;one size fits all&quot; solution beforehand. Controllers are trained to remain calm under pressure, make good choices and adapt to an ever changing environment. The day we have a set checklist for every single possible emergency situation is the day we can safely retire and let computers take over our jobs.
Further reading on SKYbrary:
Crew Incapacitation: Guidance for Controllers
Guidelines for Dealing with Unusual/Emergency Situations in ATC