Edit: This is probably the wrong community for asking this question since this community is meant for tech related news. c/asklemmy might be better or !technology@piefed.social allows for discussions on anything tech related.

Smart meters work mostly the same way meters have always worked with one minor difference, they occassionally transmit the current value via a radio frequency. Same as always, you install them at some point where they can measure just how much water/electricity/gas is flowing into the home. The transmitting frequency will be different depending on the device and what country you live in.

If you want to see the details on how water meters measure water flow, go here: https://en.wikipedia.org/wiki/Water_metering

If you want the details on how gas meters work with all of the different sensors for that, go here: https://en.wikipedia.org/wiki/Gas_meter

If you want the details on how electricity meters work, go here and read the “Electromechanical” and “Electronic” sections: https://en.wikipedia.org/wiki/Electricity_meter#Electromechanical

Some newer meters are setup to attempt to guesstimate additional information such as what is being used in your home. For instances with water meters, a small flow of water for a short time can mean the faucet was turned on, or a toilet was flushed. A larger flow for a longer time can mean that the bathtub is being used, or a shower, or an appliance (dishwasher/laundry), etc.