You can have some general idea from Ubuntu Community Documentation > 32bit_and_64bit
For more technically oriented look for wikipedia articles 32-bit and 64-bit
But I do not know whether my cpu supports 64 bit :-(
Are you on windows?
Download and install cpuz
Run it
In CPU tab, if you see EM64T (if its Intel) or AMD64 (if its AMD) then your processor is 64-bit capable.
Are you on Linux?
Type in terminal (in Ubuntu Applications>accessories>Terminal)
cat /proc/cpuinfo
In the output, in flags look for 'lm'
'lm' stands for 'Long Bit', it means your your cpu supports 64 bit...Hurrah!
My opinion
If your CPU supports 64 bit (whether Intel/AMD/Via) go for Ubunt Reloaded 10.04 amd64 even if you use 32 bit windows.