How to tell if a Windows computer has a 64-bit CPU or OS
If you are on 64-bit XP, under C:\ you will see a "Program Files" as well as "Program Files (x86)" folder.
System properties will also reflect a 64-bit OS:
Almost all processors produced since 2006 support the 64-bit instruction set, and can run either a 32-bit or a 64-bit operating system. Running a 64-bit OS requires an x86-64 CPU, but you do not need a 64-bit OS to use one of these CPUs.
Hardware
Almost all AMD processors since the Athlon 64 have supported 64-bit instructions. If you have an AMD processor, it probably can run a 64-bit OS.
Almost all Intel processors since the Core 2 series have supported 64-bit. If you have a Core 2, or Core ix processor, it can run a 64-bit OS. The only exceptions are a few of the Atom netbook processors. To check whether your processor version supports x64, look it up in Intel's processor database.
Software
Mac OS X has supported x64 since OS X 10.4 Tiger, and has been x64 only since 10.6 Snow Leopard.
There have been 64-bit versions of Windows since Windows 2000 Server, but did not enter mainstream until Windows Vista. Many computers sold with Windows today come with 64-bit Windows 7. You can check whether you have 64-bit Windows installed by going to My Computer and clicking on System Properties.
If you are running Windows XP then you are most likely running a 32-Bit Operating System, since the 64-Bit WinXP Version is extremely rare (for a good reason since it's largely unsupported).
If the PC itself is 64-Bit compatible is trickier to find out in that case. Try downloading CPU-Z and check if Instructions lists something like EM64T, AMD64, x86-64 or similar. If in doubt, please post what CPU-Z displays for Name, Specification and Instructions.