P = V I. Power (in watts) is voltage (volts) multiplied by current (amps).

So you need to measure, or calculate, the current going into the circuit, and multiply it by the voltage applied to the circuit.

You may also need to measure (or calculate) the current in different situations. The current consumption of most circuits depends on their state, which usually changes over time.

You also need to clearly define WHAT you're measuring.

For a common emitter switch, there are two current flows: the current into the base, and the current into the collector. You calculate them separately.

The base current is determined by the base series resistor. (The base-emitter resistor, if present, doesn't really come into the equation.) The current in the base resistor can be calculated using Ohm's Law, I = V / R, where V is the voltage across the base resistor (which is equal to the voltage applied to the base resistor minus about 0.7V for the transistor's base-emitter voltage) and R is the resistance of the base resistor.

The collector current is determined by the load supply voltage and the load resistance, in the same way. The voltage across the load is equal to the load supply voltage minus about 0.2V (the collector-emitter saturation voltage of the transistor).

The base-emitter voltage and the collector-emitter saturation voltage are higher if the transistor is a Darlington.

If the base current and the collector current both come from the same supply, you can add them together, then calculate the total power consumption by multiplying the total current by the supply voltage.

I hope this answers your question. If not, ask a more detailed and specific question.