I usually soak the razor in hot water. After that I place simple green or scrubbing bubbles in hot water and let the razor soak again. Usually it comes off, if it's stubborn I use a soft tooth brush along with some elbow grease and it gets pretty clean. I dry it and use a bit of polish to shine it up. I think the green stuff is called patina (I am not totally sure but someone will correct me if I am wrong) hope this helps.
+1 on soaking in hot water and then scrubbing bubbles. You'll be surprised how much gunk will simply float off while the razor is soaking in SB. Happy cleaning!
The green stuff is the metal oxidizing. Copper, which is used to make brass, turns green as it oxidizes. Scrubbing bubbles, or whatever you normally use to clean your razors should remove it.