The 12-C was the fanciest, with a crescent butplate, pistol grip, and octagon barrel. May have had a receiver peep sight, that's what the two small screws are for. The sight's a peculiar thing, and terribly expensive if you can find one.
Go to RimfireCentral.com, to the Remington section. They have a sticky on barrel date codes.
Use a coin to unscrew the takedown screw on the side of the receiver, pull the screw out as far as it will go, and the rifle breaks down (usually tight---you'll have to thump it). Next, to remove the bolt, with the rifle upside down and the slide back, depress the little button on the slide just in front of the receiver. The slide will now go back far enough to allow the breechbolt to drop into a recess and disconnect from the slide. You can then clean the barrel straight through.
These old guns accumulate crud in every recess. Use a penetrating spray to loosen stuff, then toothpicks to dig out the crud, particularly around the breech. I don't recommend disassembling the trigger mechanism, just soak it thououghly and dig out all the crud you can. Soak and clean the bolt, too. dig out around the breech face and under the extractor.
Wipe everything clean, apply your favorite lube, reassemble, and have fun. These are the snappiest pump ever made, and with a good bore shoot very well.