"When requesting VFR flight following, what phraseology should be used when contacting ATC with the request at first contact and once communication is established?" - Jan P.
“The initial call to ATC should be just the aircraft call sign and the type request. For example – Memphis Approach, Mooney five six two hotel, request VFR advisories.
After the ATC Specialist answers, give your position relative to a VOR, airport or charted VFR checkpoint, type aircraft, altitude and destination.
ATC will usually assume that you are going direct to your destination. So, unless you are doing something different, you do not have to include the routing.
Type aircraft should also be simply the basic type such as Cherokee or Bonanza.
After Radar contact is established, acknowledge any ATC instructions with your call sign and readback of the pertinent information. For example, ATC may instruct you to advise changing altitudes. If they do, simply state your call sign and intentions – Memphis Approach, Mooney six two hotel, leaving six thousand five hundred descending four thousand five hundred.“