Hey,
Get yourself some styrofoam, comfy, easy to jab things nto kind of ones.
If your CPU has pins then use this, if it isn't using pins then you can get two piece of cardboard and put one on top of the cpu and one on the bottom, celetape around it to secure the cardboard onto the CPU.
After that, get yourself an envelope (of the right size) of which has bubble wrap inside, put the CPU (with the carboard pieces wrapped around it and securely on) it's the envelope, you can then ship it off and not have to worry about it getting damaged in transit.
With the Styrofoam scenario (the pins edition of CPU), you don't really need to ddo anything else other than put the CPU pins into the sytrofoam and then put it into a bubble wrapped...