When departing a Class C airport you would normally call up clearance delivery if they have one or ground if not and request Class charlie services or VFR flight following, for example:
"John Wayne Clearance, N12345 is a P28A slant golf at Signature with bravo, request Class charlie services from 19L"
or
"John Wayne Clearance, N12345 is a P28A slant golf at signature, request VFR flight following to Las Vegas at 9500 from 19L"
They will then issue a clearance along the lines of:
"N12345 after departure, make a left turn to 170°, (climb and maintain 5500) sqwark 4465 departure frequency is 127.2"
You then request taxy as usual and after takeoff you will be told to "contact departure". There is no need for all this phacer stuff, you simply switch to departure frequency and tell them "Socal departure, N12345 2000 for 5500" and they will then give some other instructions like "Radar contact, resume own navigation, climb and maintain 9500".
Actually this procedure works from many class D airports as well (Long Beach springs to mind) especially near major airports like LAX. Just call clearance and tell them you want VFR flight following to wherever before take off, then you get handed straight to the departure controller once you have departed. Usefull for ensuring you don't bust airspace, or hit anyone else
EDIT: I just read ypou passed the PPL in FLA....so most of this stuff you should know anyway....cheers