It's not that difficult.
It is basically a little pressure sensor with an internal battery, that sends out a wireless signal indicating it's address (a unique long number), and the pressure it is sensing. This is either imbedded as a tire stem, or mounted on the inside of the rim.
In the car, is a sensor that receives those signals. Different manufacturers are different as to the approach they use, but basically it is configured (or 'learns') which address belongs to which tire position. If the TPMS computer senses a low pressure in one of the tire, it does things like turn on warning lights or chimes, or in the case of GM can also 'call home' and report it's status. I get a monthly OnStar email, listing my tire pressures and telling me they are okay (or not).