Where can I find canonical examples of radio communications at non-towered airports?
What you're looking for is AIM 4-1-9(g)(6), recommended self-announce phraseologies. The self-announce phrases states position, altitude, climb/descent, among other things depending on the situation.

6. Recommended self-announce phraseologies:
It should be noted that aircraft operating to or from
another nearby airport may be making self-announce
broadcasts on the same UNICOM or MULTICOM
frequency. To help identify one airport from another,
the airport name should be spoken at the beginning
and end of each self-announce transmission.
(a) Inbound
EXAMPLE−
Strawn traffic, Apache Two Two Five Zulu, (position),
(altitude), (descending) or entering downwind/base/final
(as appropriate) runway one seven full stop, touch−and−
go, Strawn.
Strawn traffic Apache Two Two Five Zulu clear of runway
one seven Strawn.
(b) Outbound
EXAMPLE−
Strawn traffic, Queen Air Seven One Five Five Bravo
(location on airport) taxiing to runway two six Strawn.
Strawn traffic, Queen Air Seven One Five Five Bravo
departing runway two six. Departing the pattern to the
(direction), climbing to (altitude) Strawn.
(c) Practice Instrument Approach
EXAMPLE−
Strawn traffic, Cessna Two One Four Three Quebec
(position from airport) inbound descending through
(altitude) practice (name of approach) approach runway
three five Strawn.
Strawn traffic, Cessna Two One Four Three Quebec
practice (type) approach completed or terminated runway
three five Strawn.

Examples shown are from the Aeronautical Information Manual. I hope that helps!