What is the exact dialogue a crop duster pilot will have, if any, with ATC on a routine flight?
The actual operation of a crop duster airplane will almost invariably happen in uncontrolled airspace. In the US, controlled airspace does not start until 700, 1200, or in a very few select areas 14,500 feet above ground level; below that the airspace is Class G, uncontrolled. Crop dusters operate at a few hundred feet above ground level or lower (a quick google shows altitude as low as a few tens of feet AGL). Even if they wanted to talk to ATC at those altitudes, radio reception would be all but impossible.
When not actually working on a field crop dusters must adhere to the standard minimum altitude rules (500 feet AGL over non-congested areas, or 1000 feet above the tallest obstruction within 2000 feet over congested areas). But even if they enter Class E airspace, which is controlled, they do not have to contact ATC unless they want to receive an instrument flight rules clearance.
There are three times when a crop duster would have a dialog with ATC: when they want to come into a controlled airport to land, when they want to transition the airspace close to a controlled airport (where the controlled airspace extends to the surface), or when they want to operate over a field within the controlled airspace near an airport. For the first two situations they would communicate with the tower just like any other aircraft; for the last situation it might sound like this:
Duster: Podunk Tower, hello, Air Tractor 123AT is eight miles to the east, we'd like to operate over a field inside the Class Delta airspace two miles east of Podunk Airport.
Tower: Air Tractor 123AT, Podunk Tower, the Podunk altimeter 2992, proceed as requested and remain east of runway 18/36.
Duster: Proceed as requested, remain east of 18/36, Air Tractor 3AT.