I'm trying to find any canonical examples of radio communication patterns at non-towered airports. The FAR/AIM has very little in terms of sample announcements, etc. The AC-90-66B (https://www.faa.gov/documentLibrary/media/Advisory_Circular/AC_90-66B.pdf) doesn't offer much either. The best resource I could find so far is the "Say Again, Please" book by Bob Gardner, but I'm trying to find the guidelines from the "FAA's mouth."
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.
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.
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
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!