You answered your own question! It's that simple. I did it a long time ago for pasta I think, and since I could not remember the finer points of the technique, allow me to refer you to Thomas keller's explanation.
In a nutshell, he pulses the greens (spinach and/or watercress/parsley) in a robocoupe (or push through a grinder), add 4X the volume in water and soak overnight. Strain the water in a pan, squeezing all the moisture out, and bring to a boil, stirring constantly. When it's fully separated, cool quickly with some ice and strain through a cloth overnight. This will keep for a couple of days only.
In one of the restaurants I used to work at, we pulled chlorophyll quite often. To do it, we packed a blender cup with fresh spinach, filled with water and pureed it until the water turned a deep green. We then strained the water through a chinois, poured it into a pot and slowly brought it to a simmer. As it comes up to a simmer the chlorophyll coagulates and rises to the surface. We skimmed this off, and allowed it to drain through a coffee filter. We used it for coloring a variety of things (including our hair one very boring day at work!!!) and would freeze it in small packets if we made more than we needed.
I used to buy the stuff at a health food store. If you dilute it in water and drink it, it is supposed to work wonders in your body. Do you think that would be the same stuff without the fuss of doing it at home or is it something completely different?