Most appliances will have a label or include a manual with the wattage. Some may also have amps too. But it's simple Ohm's law: volts x amps divided by ohms = watts (power).
So if an appliance uses 1200 watts of power plugged into a 120 volt outlet, ignore the ohms and simply divide the 1200 by 120 and that's your amps, in this case 12 amps of current flow.
In the case of say a dryer, it may use 7200 watts of power (240 volts x 30 amps) on high heat. After it reaches temperature, the thermostat will turn on and off to maintain temperature as well as some models may use a variable amount of wattage to maintain temperature rather than an all or nothing heating. A room fan with 3 speeds is likewise, three fixed amounts of power used.