There are several ways you can do this.
1) Buy a 4-wire meter.

2) If you have 2 DMM's, you can use one to measure the current and the other to measure the voltage drop across the load and then use Ohms law to get power.
3) Use the above method with a known precision shunt resistor value.
If you want to get variable power usage and total, you can use data logging software and import this into a spreadsheet then perform the calculation for power at each point to get the total power. It take a bit of math but not too hard. The faster the sample rate the better accuracy you will have.
If I get more time later today, I can detail the process a bit more.