I actually thought my Whites were easier to get at all the stuff in the "head" part than the Singers. The "head" came off with a couple of screws. There are pictures on Treadle On. I didn't remove anything from the head itself except the tensioner, the small caps on the top covering the needle and presser bars, and the small thread guide on top when I cleaned mine. I took off the small parts like the spool holder to clean separately. Everything else stayed on, including the hand wheel--those weren't really made to come off. I had one that was in pretty poor shape, so I did go through a whole kerosene soak, scrubbing the parts that I could reach. The kerosene looked like motor oil when I was done. This may not be necessary if your machine hasn't been kept in terrible conditions for 80 years!
As a word of caution, I have found that the finish on the machine was a lot more fragile than that of my Singers, so be careful of the decals.