They are available in various wattages, and I have two, both 50W, one with a nice fat screwdriver type tip, for valve stuff and tagstrip etc, and a slender one, for more delicate work.
The tip has a temperature rating stamped on it's base. This contains a special magnet, which loses it's magnetism at a certain temperature (known as Curie temperature). This magnetism is used to operate a magnetic switch (like a reed switch, but a little more robust) to switch the element on and off, which heats the tip.
As bench space is limited, I only use one power supply, and got sick and tired of pulling one iron plug out of the power supply, and plugging the other in when I wanted to switch between irons. What was needed was a switch box....
... then I got a bit geeky (well, there's a surprise!). Let's have an led on the box, to show when the iron is heating. Useful to know if the iron is up to temperature, or if a fault has occurred (occasionally the switch or element fail , see here ) , so I devised a simple circuit to put an LED on when the iron is drawing current.
Simple. When the iron is drawing current, there is a small voltage dropped across R1, which causes the op-amp IC1A to attempt to drive it's output to rail. Now the current flowing in R1 is obviously AC, so the output is a 50Hz (or 60Hz, depending on your mains) waveform, but it's enough to light a red LED. The power supply for the op-amp is a crude supply derived from the 24VAC from the weller PSU. It's half-wave rectified by D1, and D3 and R2 Clamp the voltage peaks to 5.1V. It's smoothed by C1.
It's crude, horrible but works!