First of all: Get ATIS if provided, then
Listen and
Wait for end of conversation -- this may require patience as others tell life story
Following the less is more rule:
xyz twr, Cessna FABC with Xray
Cessna abc, xyz twr
Cessna abc somespot 4.5 Northbound
Cessna abc, altimeter 29.99, report leaving the zone.
29.99 abc
.
.
.
xyz twr, Cessna abc departing zone Northbound
Cessna abc, cleared enroute, [have a good day]
[And a good day to you]
I leave initiative for pleasantries or chat to the twr as their workload permits.