Pilot can make request to air traffic control, but are subject to operational demands of the airport as a whole.
Air traffic control works behind the scenes with airline dispatch offices to let them know what STARS and approaches are in use. Dispatch would file the flight plan with ATC.
Then, in the plane, pilot would load into FMS as assigned by clearance delivery, which might be the filed flight plan or something else, depending on what else is happening- weather, closed airport reroutes etc.
Use the CRAFT mnemonic in the US
C- cleared limit (destination or where to expect further clearance)
R- route of flight
A- altitude
F- Departure control Frequency
T- transponder squawk code
Clearance Delivery: Airplane 123, cleared to OHare. (C)
Takeoff runway 13R, Kennedy 5 departure, direct HEROS, direct SAX, then as filed. (R)
Climb via the SID, Canarsie Climb (A)
Departure on 120.55 (F)
Squawk 2627 (T)
(After readback)
ATC: Airplane 123, read back correct, contact ground for taxi.
Airplane 123: Kennedy ground, Airplane 123 at B12 ready for taxi, IFR to OHare
Ground: Airplane 123, a bit of a backup at 13R, expect runway change to 13L, no change to your clearance other than runway. taxi instructions
An airline would be able to handle much of the “dialing in” electronically, pulling the route from Dispatch office.
They would then get the clearance (these days) electronically instead of by radio and would get the print out from the Flight Deck computer. Electronic clearance delivery usually with FANS datalink to ATC. If the plane does not have FANS or something is not quite right, they would get it the old fashioned way by radio as above.
The crew would then go way point by way point to ensure that the flight plan loaded into the FMS is the cleared route and make amendments as needed. In some cases (complete reroute after PDC issued), they would have to dial everything in if needed.
A GA pilot would dial everything in with knobs and buttons.
(US experience only)