The FAR/AIM chapter 4, section 2 defines the general framework for radio communications. Starting with the facility being called, then your full aircraft identification, state your position when operating on an airport surface, type of message to follow or your request itself if it is short. Here are some examples that I’ve encountered so far.
Just before starting to taxi out of the hangar after receiving a weather briefing (Yankee)
Livermore ground, Cessna 2 5 Echo Sierra Northeast Hangars taxi for takeoff with Yankee
Ground responds
Cessna 2 5 Echo Sierra Livermore ground runway 2 5 right taxi via Bravo
Pilot’s acknowledgement
2 5 right via Bravo 5 Echo Sierra
After getting to the run-up area and completing the pre-takeoff checklist
Livermore tower Cessna 2 5 Echo Sierra 2 5 right ready to go right downwind
Tower responds
Cessna 2 5 Echo Sierra Livermore tower number 2 for departure hold short of runway 2 5 right
Pilot acknowledges
Hold short 2 5 right 5 Echo Sierra
Tower asks to wait
Cessna 5 Echo Sierra runway 2 5 right, lineup and wait, traffic in the pattern
Tower gives clearance for takeoff
Cessna 5 Echo Sierra, the upwind traffic is in the right pattern, right downwind approved runway 2 5 right, cleared for takeoff
Pilot’s acknowledgement
Cleared for takeoff 2 5 right, 5 Echo Sierra
Approaching Byron for a landing. It is a non-towered airport.
Byron area traffic, Cessna 2 5 Echo Sierra is over Discovery Bay, inbound for right traffic runway 3 0, Byron
Approaching Byron airport for a landing. It is a non-towered airport.
Byron area traffic, Cessna 2 5 Echo Sierra is on the 45, inbound for right traffic runway 3 0, Byron
At Byron airport, getting ready for a takeoff followed by a landing. It is a non-towered airport.
Byron area traffic, Cessna 2 5 Echo Sierra is taking runway 3 0 for right closed traffic
Ready for a takeoff from Byron, heading to Livermore and on the way flying midfield over the runway. It is a non-towered airport.
Byron traffic, Cessna 2 5 Echo Sierra is taking runway 3 0 for an overhead 2 7 to Livermore
Flying over midfield over Byron airport. It is a non-towered airport.
Byron area traffic, Cessna 2 5 Echo Sierra is crossing midfield at 1200
Approaching New Jerusalem airport to check the runway, traffic pattern and wind direction. It is a non-towered airport with nobody around at the moment.
New Jerusalem traffic, Cessna 2 5 Echo Sierra is about 3 miles to the northwest inbound for an overflight for wind check
After circling the runway in a left traffic pattern, we announce our location.
Cessna 2 5 Echo Sierra is left crosswind to runway 3 0 New J