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This is tricky, as power is calculated as voltage x current. Measuring (or knowing) voltage is usually pretty straightforward. But accurately measuring current requires setting up the circuit so it flows through the multimeter (while set to whatever current measurement mode it has - usually "Amps A/C", or similar). However, this method isn't safe, or practical, for non-electricians to measure A/C appliances.
As someone else mentioned, you could buy a multimeter that has an "amp clamp" - effectively a non-contact way of measuring current. BUT, you need to be aware...
A typical appliance's cable will have both active and neutral wires inside the outer layer of insulation. Current flows through a circuit - up one wire and down the other, if you will. So an amp clamp can only measure the current on one of those wires. If you were to measure both at once (ie. clamp the whole cable), the readings in each direction will cancel each other out. You'll measure zero net current. The only way is to cut the outer insulation and clamp a single wire inside.
I would absolutely NOT recommend this for an A/C appliance. The possibility of accidentally cutting through the insulation of one of the inner wires, combined with the possible death of the person handling it afterwards, should make this a non-starter.
Your safest options for ANY A/C powered appliance are to either:
There's many, many brands for the latter available, and most are really quite affordable.
Edit: as another commenter said, you could possibly buy a short extension lead that splits the wires out for you, but now you're buying a non-standard extension lead and (possibly) a new multimeter, all to validate what's on the appliance's label.
A $20 smart plug with current measurement will still be your cheapest and safest option.