Read http://support.microsoft.com/kb/2118008 , and download the Microsoft Money Deluxe Sunset install file onto the new computer. Install.
From the old machine, copy your *.mny and your latest *.mbf files to the Documents folder of the new computer. Open Money by double-clicking the *.mny in Windows Explorer.
Once inside, in Tools->Settings->BackupOptions, for your upon-exit backup file,
Browse to your Documents folder, and choose a filename for your
backup; the file location remembered from your old file probably
does not exist on the new computer. I suggest you plug in a USB
flash drive, and Browse to that for the location for your scheduled
backup.
Review your backup policies. Periodically copy your newest *.mbf
file to other media, in case your hard drive fails or your Money
file gets corrupted somehow. You don't want to overwrite your only
good backup file by backing up a corrupted Money file over it.