What do you tell someone new to going oncall or PagerDutyl?
There are a number of things that I think it's important to know before going on-call:


How to triage an issue.  There should be a defined list of priorities with examples so that you can identify how serious a problem is.
What the priority levels mean.  Can you ack this and then go back to sleep?
Who to contact post-triage. The on-caller's primary responsibility is triage, not fixing.  Fixing the problem is good, too, but once you've triaged the issue, then it's up to you to rope in other folks from other teams and manage communications between them.


People jumping straight into fixing problems before triaging is the most common mistake I've seen (because, after all, we're used to fixing things and think of that as our job).  But communications are often vital, and doing things in the wrong order can mean customers are left in the dark because you got caught up in trying to fix a problem before letting your support people know there is a problem.