This Gruen Patent from 1972 is featured not because it's particularly groundbreaking, but because it does such a great job at showing one common way to implement day-date mechanisms.
The day indicator is linked to the seven-sided star gear shown in the center, and it's advanced by the wheel to its left with a single finger. That wheel rotates once a day, and once a day rotates the star gear by 1/7th of a rotation, advancing a day wheel that shows the day of the week on the face of the watch.
Meanwhile in this implementation, the finger in the lower left will connect with the spurs on the date wheel around the edge. As it completes its rotation, it will advance the date wheel just like the date wheel does.
This particular implementation has a couple of interesting tweaks. The date cam is in a groove, so as it rotates around it also extends out a bit to better engage the spur. It also keeps the two wheels (day star wheel, and date wheel) in place with springs, that aid in limiting the movement to once a day when engaged by their respective cams.