In order to use it, you have to stand in front of the structure you want to remove the paint off. Press E and click on the respective button in the wheel menu. Using Soap by equipping it to your hotbar will poison you. To remove dye from an item (like armor) drag the soap over it.
If you take the soap and grind it in an industrial grinder, you will get organic polymer in return, allowing you to use soap as a storage method for organic polymer, as soap doesn't expire.
You can acquire the engram through admin command by changing the last 0->1: GFI Soap 1 0 1
Since each soap is used once, it can be a very expensive way to clean more than several structures. A much cheaper alternative is simply paint over with a Paintbrush or Spray Painter or replace it.