You can measure current draw of some appliances, but other appliances have an On-Off cycle. Those could use some kind of time-logging device.
I tracked my refrigerator cycles with my VIC-20 computer. I constructed a homebrew circuit for detecting AC current which then sent a voltage to the computer's game port. I wrote a program to record On-Off events. After running a few hours it told me the appliance drew large current for a few minutes, then was off for several minutes.
I thought of attaching a voltage detector on the motor but I had no easy access. If you are careful around high voltage you might make a voltage detector which indicates status of water heater elements, or a furnace, etc.
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Another indicator is your electric utility meter. Maybe it has a rotating dial, or maybe a digital display. Watch how fast it advances to get an idea of your power usage.
To read AC current with your multimeter, insert a resistor in series, and measure AC voltage across it. I have several 1 ohm 10W resistors (rectangular sandstone type) which I connect in series or parallel, in order to create a low ohm value which permits a sensible reading. Usually I need to work fast because the resistors heat up quickly.