What is the correct method for installing a 32-bit version of Windows Vista on a dual core 64-bit processor?

To install a 32-bit version of Windows Vista on a dual-core 64-bit processor, the appropriate method is to install the operating system normally. A 64-bit processor is capable of running both 32-bit and 64-bit operating systems, which means it will have no issues executing a 32-bit version of Windows Vista. During the installation process, if you have the correct installation media, the system will recognize the processor architecture and allow the operating system to be installed without needing special settings or modes.

Using compatibility modes or creating a partition is not necessary for this scenario, as a straightforward installation of the 32-bit OS will work seamlessly on the 64-bit processor. Installing a 64-bit version first is not a prerequisite either; you can directly install the desired 32-bit version independently. Hence, installing the OS normally is the correct approach in this case.