what is required to convert a Dell Optiplex 780 with 32 bit OS to a 64 bit OS?
my Dells:Precision M6300 - Windows 7 / Ubuntu 12.04Latitude D620 - XP Pro SP3Precision M6300 - Windows 7 Pro 64-bit / Windows 8.1 Pro 64-bit
Just 64-bit installation media ... your system should already be 64-bit compatible. Only thing to watch out for is other incompatible hardware or software (although nearly all software that runs on 7x86 runs on 7x64).
Get drivers from here, start with System Software, then Chipset: