You can get USB power meters that you simply plug into the USB cable between the computer and the Arduino.
In order to measure the power you need to measure the current and voltage at the same time. It is difficult to measure the current when you are using the USB connection so it may be better to supply the unit from the 5 Vcc connection (if your Arduino uses 5 V).
Also note that when using the USB as power supply a fair amount of power is used by the voltage regulator. Depending on what your Arduino is actually doing the power used by voltage regulators, LEDs, etc. can be much larger than what the Arduino uses.