Open the Terminal and type the following command:
uname -a
If you’re using a 32 bit Kernel in Mac OS X:
iMac:~ user$ uname -a
Darwin iMac.local 10.0.0 Darwin Kernel Version 10.0.0: Fri Jul 31 22:47:34 PDT 2009; root:xnu-1456.1.25~1/RELEASE_I386 i386
see the i386 on the end there? That indicates it’s the 32 bit kernel
If you’re using a 64 bit Kernel in Mac OS X:
iMac:~ user$ uname -a
Darwin iMac.local 10.0.0 Darwin Kernel Version 10.0.0: Fri Jul 31 22:47:34 PDT 2009; root:xnu-1456.1.25~1/RELEASE_X86_64 x86_64
the x86_64 at the end will let you know you are using the 64 bit kernel.