Are you planning on taking apart the tension assembly? From your picture I would dial it out all the way, push in the numbered dial from its edges, then unscrew the thumb nut the rest of the way, there is likely a little pin on the underside of the thumb nut that locks it into the numbered dial. If the thumb nut does stop when you back it out, then there is likely a small washer underneath with a little bent finger on it, you have to pay close attention to which way the finger bends. You'll see how the discs come off. This is usually sufficient for most cleaning
Usually to remove the spring you have to remove the whole assembly, or unscrew the main post. There may be a set screw on either side of the assembly holding in an internal housing, or the main post may screw into the housing cast into the body. This gets a little trickier if you remove it because the check spring is under some tension and it has to be put together again with the right amount of tension, it can't just float loosely.
As noted above, take lots of pictures as you go.