With a smart metering system, the readings are transmitted automatically. With a consumption below 100,000 kWh a year, it transmits values in 15-minute intervals once a day. You are entitled to a free monthly overview of your consumption and costs. A photo of the display still does no harm, for example when you move out.
For gas, the supplier converts the cubic metres read into kilowatt hours using the calorific value (Brennwert) and the conversion factor (Zustandszahl). As a rough rule of thumb, the consumer advice centre says: cubic metres multiplied by ten gives roughly the kilowatt hours. This way you can roughly estimate your consumption yourself.
When you move house, report moving in and moving out in good time. According to the Federal Network Agency, a new electricity supplier cannot be assigned retroactively. For gas, this is only possible in exceptional cases if it was agreed in advance, and for no more than six weeks. If you move in and do not have a contract yet, you are supplied by the default supplier (Grundversorger) at first.
Self-reading (Selbstablesung): your supplier may ask you to read the meter yourself. If this is unreasonable for you in an individual case, for example because you cannot reach the meter due to an illness, you can object. The supplier must then read the meter itself without an extra charge (§ 40a Abs. 1 EnWG).