You can use the command "uname -a" to show all of the kernel identification information. For example on my current system:
tj@T-Bird:~$ uname -a
Linux T-Bird 2.6.24 #1 PREEMPT Wed Apr 9 10:37:19 EDT 2008 i686 Intel(R) Pentium(R) 4 CPU 2.40GHz GenuineIntel GNU/Linux
Here you can see the hostname, kernel version, the machine type, and finally the processor itself. You are interested in machine type, which in this case is "i686", meaning 32 bits.
You can see just the machine type with "uname -m", as well.