It is easy to do, you already know the program you need to use, it is "Process Monitor"(procmon.exe), you just need to use different filters.
First you need to set the filter to include the program you want to monitor by either set:
PIDis$pidthenInclude
$pid is a placeholder for the actual pid, i.e. 7552
or: Process Nameis$namethenInclude
$name is a placeholder for the actual process name, i.e. explorer.exe
You can get process name and pid through Task Manager(taskmgr.exe), by left clicking "More details" then right click on resource values bar and check "PID" and "Process Name".
Either of the about two options will work and they have the exact same effect, they will make procmon display only activities of the process, the difference is PID is variable and may change every time the process launches, but it may be easier to type. The process name may be harder to type but is invariable (unless you rename the executable).
Then you need to set the filter OperationisWriteFilethenInclude to display the file changes made by the process. WriteFile is the operation recorded when a file is modified.
Then click Apply and then OK to make the filter take its effect.