To get the fork tubes separated, you need to get an allen type wrench on the bolt that is visible at the bottom of the slider, and then a 13mm socket on about an 18 inch extension to get the hex shaped top of the damper inside.
I use an allen wrench socket instead of an L shaped wrench, gives you something larger to hold onto, instead of an allen wrench, and a bit less prone to slipping off of the bolt head.
You can use just about any type of cleaner to clean up the inside of the tubes.