My strategy with ATC is to keep it brief and let them tell me things or ask questions. With practice you will know what they want in different situations, but I start off with:
Me: XXX Approach, NYYY, request. [To get their attention]
App: NYYY, say request.
Me: NYYY is a Cessna something, departed/over location/landmark/fix. [Tell them where you are so they know you are on the right frequency/sector] Request flight following. Making a circle around the Class C. [Briefly say your intentions.]
App: [Here’s where they will elaborate, and hopefully say squawk ZZZZ.]
In general, ATC is your friend. If you can do it, instrument training makes this second nature.