In order to get points you need to hit the enemies while having picked up the matching color. Once you have picked a color you can go to one of the two palettes and press E to mix two different colors.
Simple colors (yellow, red & blue) give 10 points, while mixed colors (green, orange, purple) give 100 points.
There is also a "how to play" within the controls screen in the options menu. A little too hidden, I guess :(