On Unix-like OSes you can type
uname -m to show the architecture:
$ uname -m
Under Windows follow Microsoft's guide:
To find out if your computer is running a 32-bit or 64-bit version of Windows in Windows 7 or Windows Vista, do the following:
Open System by clicking the Start button, right-clicking Computer, and then clicking Properties.
Under System, you can view the system type.
If your computer is running Windows XP, do the following:
Right-click My Computer, and then click Properties.
If you don't see "x64 Edition" listed, then you're running the 32-bit version of Windows XP.
If "x64 Edition" is listed under System, you're running the 64-bit version of Windows XP.