How to process images into simple colors?

Under Color on the menu, there's normally an option for how many colors are allowed, as few as 16. GIF allows a maximum of 256 colors (8 bit) but you can use a lot fewer. If your image editor has the option of changing the number of colors, if you reduce the number, it will ask you how to choose the new colors - like nearest match, etc. - and you will have to play a bit to see what the effects of choices are. Once you have reduced the colors of the photo, you can use the color changer to change your choices and sweep across the selective brush.

As similar to video part where dots are used to make color image,

you can try photoshop halftone filter and apply your own colors,

http://www.photomatters.org/computer-filters

if you wanted minimal color areas then to try posterizer

http://www.crestock.com/blog/photoshop/photoshop-tutorial-constructivist-propaganda-poster-159.aspx

you can make colour map of image and that create palette for colors in that image,

you could pixelate image to change to square dots,

you could trace bitmap in Illustrator
http://urlnextdoor.com/arc/interactive-media-flash/week04.php