How does one find postdoc positions after completing a physics Ph.D.? Does there exist a central website listing opportunities?
There is no clearinghouse or standard way of advertising postdoc jobs in Physics. Opportunities may be advertised on the Physics Today Jobs or Nature Jobs websites. But more often they are listed on an institution's job website or a research group website. Positions may be advertised on mailing lists. Some just are not advertised at all. You have to ask.
I had the same problem when I graduated. What I was advised to do was to search online for advertised postdocs. I knew from papers and conferences some people in my field, so I would go to their web pages and send them an email if I saw them advertising a position. Sometimes, I would send them an email anyway asking if they had an open position. Some woudn't answer at all some would tell me they had no money at the moment, and a small number of them were interested.
If you do that, you need to write a short email that highlights what you can do for them. You should ask your friendly faculty/adviser how to write that properly.
Another path is using connections. Your adviser/friendly faculty know people in the field. Sometimes they even write each other emails advertising an open position and asking if the other doesn't have someone graduating. Or the other way around. Or you could have your own friends/acquaintances/collaborators in your field and could ask them if they know of any open position.
A third solution is to advertise yourself at conferences. You give your talk, and after the conclusions, you show a page where you put contact data and tell the audience you're graduating soon and you want to find a postdoc position.
I personally used the first and second method. The first method got me 3 offers, and the second, 2.
As far as online resources go, I can add this one, which I used in the past.
There are websites listing open positions advertised by universities and institutes. They are not physics (or postdoc-level) specific, but they tend to be easily searchable with many predefined keywords. Examples (that I know of) are:
These examples tend to be Europe oriented, but they are not exclusively so - you can find posts from across the globe. There are also ads for tenure track positions as well as fellowships, grants, etc. All-acad.com will also send you customised weekly digests via email.