what is required to convert a Dell Optiplex 780 with 32 bit OS to a 64 bit OS?
my Dells:Optiplex 3020 - Windows 7 Pro 64-bitPrecision M6300 - Windows 10 Pro 64-bitPrecision M6300 - Linux Mint 17.3 Rosa / Ubuntu 12.04.5 dual-bootLatitude D620 - XP Pro SP3
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: