Based on my time working as an engineer working for http://www.coolitsystems.com/" , here's what I've learned:
This is/ can be actually really difficult to determine depending on what your reasons for wanting to know what the power of a proc. is.
If you don't need a terribly accurate guess, say within 15% going by the thermal design power (TDP) of the processor will probably be fine. Note, this number will only be valid when the processor is loaded at 100%, even then the actual power will be a little bit lower than the TDP.
If, however, you need a more accurate power or you have overclocked the processor, or it isn't running at 100% then you need to get crafty.
You can get a more accurate measure of the power of the processor by probing the current going into the EPS rail of the motherboard. There will be a number of yellow and black wires going from the power supply to the motherboard near the processor. You need to cut the mesh sleeve of the wires and use a clamp meter on the yellow wire, make sure you get all of them and none of the black wires (this is the reason for cutting the sleeve). This supplies 12V to the switching power supply that steps to voltage down to about 1.3V for use by the proc.
Of course, this number won't be the actual power going into the processor, you need to account for inefficiencies in the aforementioned switching power supply, say 85%-90%. This will get you to within about 5% of the actual power dissipation.
If you need to get any more accurate than this you would need to probe the current of every single ground pin on the processor. This is not a practical solution.
Depending on the processor expect power level from about 50W for a low power desktop processor all the way up to 220W for a high end desktop processor.