How much help should one expect from their PhD advisor to get a job (academic or industry)?
I think it's reasonable to expect a PhD advisor to make introductions but not to place you into jobs.
They should help introduce you to people at conferences, both directly 1 to 1 or by supporting you in getting opportunities to present.
They should introduce you to visiting professors when they come to tour your space/give a talk to your department.
They should involve you in collaborations, to expose you to more ongoing research as well as researchers.
When it's time to apply for a job, you should make the phone call (or often an email). The introductions you've already had let you start the conversation with something like:

Hi, I'm Professor Maxwell's student, we met at the Demons Conference last year. I'm graduating this year and looking for post doc positions...

For industry jobs, I think it depends on your lab and your advisor. For some labs, your advisor has industry as well as academic contacts, because you collaborate with industry or work in a field where industry researchers are found at the same conferences as academics; in that case, all of the above still applies. For others, I would expect you would need to do more outside networking on your own, and I would look more to the rest of your institution for the same sort of networking support, through job fairs and such.
In some locations and cultures, yes, maybe a phone call is all you need, but in others people would be offended by that approach. The phone call that is more important to get you a job, though, goes the other way: it's when the future employer calls your advisor after hearing from you, and asks them what they think of you.