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Take the bolt head off - that will give you access to the firing pin and spring. There really is no need to disassemble the bolt further if you use brake or carburetor spray cleaner.
Check the extractor for wear and gunk under it.
TAKE IT OUTSIDE. Wear goggles, rubber gloves and a face mask. I prefer carburetor cleaner to brake cleaner for a spray application. Attach the spray tube to the nozzle, aim away from you, put the tube down inside the bolt body, making sure the spray will exit away from you, and give it a good shot. Do the same with the bolt head.
When lubricating the cleaned bolt, make sure you use a good GUN OIL, not stuff like 3 in 1. Do not over lubricate as oil tends to thicken during the winters, and can slow down the firing pin spring.
On Military rifles, too many people tend to over disassemble the parts, even down to the last screw. This is not really needed, as these rifles were designed for rough use and very simple maintainence procedures. More advanced procedures were left to Unit Armourers who had the tools and equipment to do the job. Actually, the only really good reason for completely disassembling the SMLE or LEE-Enfield bolt is to replace broken parts such as a firing pin, the firing pin spring, the extractor or the extractor spring.