A sketch for the Arduino is a .pde file that contains only a portion of the program. There is no main(), for instance.
The sketch can include .h files. When the Arduino IDE's Verify button is selected, there is a lot of stuff that happens. A .cpp file is created, with function prototypes for all functions defined in the .pde file. A main function is added.
Then, the compiler is invoked. A pre-processor is run to deal with all the #include, #define, #ifdef, etc. statements. Then, syntax parsers and a variety of other functions are invoked, to make sure that the code is valid, to allocate storage space, to convert the C statements to assembler instructions, etc.
A number of other .cpp files may be compiled, too. The end result is a .o file.
Then, a linker is invoked to combine the appropriate sections from the .o files, perform memory translation, optimization, etc., resulting in a .exe (or .hex for the Arduino).
The intermediate files are not stored.
If you want to capture all the intermediate files, there are compiler options to do that, but they are not set by the Arduino IDE.
There are ways to invoke the compiler directly, and set the compiler and linker options. The resulting .hex can then be uploaded to the Arduino, but not by using the IDE.
There are tools for reading the .o files, which can reveal a lot about how the compiler works. There was another thread recently that had some links.