I am replacing my White-Rodgers 1F76-357 thermostat, but I need to know whether I have a one or two transformer system.

2 transformer systems are usually more complicated systems, often one where additional devices were added later. As for identifying one, I guess looking around the system for a second one, or additional wiring, and comparing your existing wiring to the examples in the directions for the new thermostat.

I do not understand the need for a second transformer in most cases. Since you don't run the heating and A/C at the same time, most transformers will have the capacity to run one or the other at a time.