On mine, the white paint on the face was also _very_ fragile. Later cars are apparently better in that regard. The best method I found was to not get the white letters and marks wet at all (even water was taking off the paint). Instead I used an artist's brush to lightly brush the entire face dry, then dampened it to clean the background up to the edge of the letters. Last time around, I used Pledge as the solvent, hoping it might help keep it cleaner longer in service.
To do just the face, you can just remove the bezel and glass. But at the least, I'd want to remove the mechanism and paint the inside of the housing. It lights up a lot better at night with a fresh coat of white paint in there. To effectively clean and lube the mechanism, though, requires a fair amount of disassembly. With care, you can leave the mainspring attached at both ends, but I wound up disassembling pretty much everything else. Here's a few shots I took:
https://s258.photobucket.com/user/TR3driver/library/Speedometer repair
Be careful when you remove the needle; I've managed to break a shaft just pulling on it. A twisting motion (while holding the aluminum cup so the shaft can't turn) may be the best way, but I've had good luck using a pair of screwdrivers, one under each side, then twisting the screwdrivers to apply upwards force on the metal hub (not on the flimsy metal that forms the visible part of the needle). Fortunately I've got several spares for parts (which is where that rusty case in some of the photos came from).
And as I think Tony mentioned in the article I linked to above; you will probably need to replace the rubber seals around the glass. I unfortunately forgot to document the sizes, but found some O-ring stock that I was able to cut and glue to the right size. I also put an O-ring under the outer ring that deflects the light (and painted the back of it white).