The modern version is based on capacitive touch. The older versions with the stylus required were mostly resistive where there were two layer matrices in X and Y directions and the crossed resistive connections are calculated. There was also an in between rarer version of the touch screen that was optically driven. These require a special stylus that technically does not need to make physical contact to work, (it was crap compared to capacitive touch).

If you were around back in the day of rabbit ears and television or had a radio that would only work well when you were in just the right spot in the room while you held your tongue at the right angle, that is basically the same principal of capacitive touch. Your body’s electrical properties are more pronounced at higher frequencies and this effect is used to detect where changes are happening on an X/Y matrix.

The actual connections are a tin oxide coating on the glass that is conductive but so thin that it is optically clear. Ben on Applied Science on YT has shared some videos where he uses this same coating technique for various projects.