Plotting dots is nothing more than plotting single pixels somewhere on the screen. This can be done either in character mode or in hires mode. Char mode can be easier to calculate, because of the order of the bytes on the screen, while hires offers more space to plot in.

The main challenge is to make a routine that is able to plot two or more pixels in the same byte independently. This is done by performing a bitwise OR on the already plotted pixel and the one to be added.