I have CS3 Production Premium on a first gen intel Mac Pro and I just purchased a new Mac Pro, how I move the Adobe Suite to the new computer?

Assuming the process is the same on a Mac as it is on PC: deactivate all software using activation technology on the old machine, then install and activate on the new machine.

Again, if it's the same as a PC, you don't need to deactivate the old machine unless you are getting rid of it. Adobe allows concurrent licensing on a maximum of two machines.