Usually there is a sticker on the machine if it's 64 bit. If you don't have that it appears to be very hard to tell. Looking on the web it seems like you can only tell if the OS you're running is 32 or 64 bit.
One of the easiest ways to tell would be to try installing a 64 bit OS. If you have 32 it won't install, if you try it the other way, a 32 bit OS will install on the 64 bit processor just fine.
Another way to tell is if you have stickers on the pc that tell you what kind of processor you have and do a search at the manufacturers website to see if they only made that processor in 32 or 64 bit.
The main difference between the two for end users is that you can access more RAM from the 64 bit machine; you'll usually only get around 3.15GB of RAM usable even if you have more than that installed. The 64 bit is only limited on desktops by the number of slots you have for RAM and the amount of RAM that will fit on each chip that the MB can handle.
I hope this help answer your question.
Addendum - after posting I saw that others had asked questions and your answer of 512M of RAM tells me you almost certainly have a 32 bit machine.