One method, which is not very accurate but is very easy, is to look on the back. Most appliances, or their power supplies if seperate, will have this info printed on their back. In some cases (e.g. Simple appliances such as An electric heater or tumble dryer) this will be the power that they actually use, and in some (eg a computer) it will be the maximum rating of the power supply, and thus only an upper limit that may never be reached.
Sometimes the power is given in watts. Sometimes, instead, the current draw is given in amps (A) or milliamps (mA) (there are a thousand milliamps to an amp). In this case, multiply the current by the voltage where you are to get the power .
For example, most of Europe has mains electricity at 230V, so if the label said "input: 200mA" you would do 0.2 × 230 = 46W.
Having said all this: for many purposes, you are much better off with a meter :-)
 for the pedants, I'm deliberately ignoring power factor. Most domestic electricity meters ignore it too.