Here are a number of options that have been used by players for a long time. Some individuals do not recommend one or more of these; others swear that their preference is the only and best cleaning solution. Do not apply any of the abrasives or pore fillers on fiberglass, graphite, or laminate cue shafts.
Scotch Brite green scouring pad - this is a slightly abrasive pad that you wrap firmly around the cue shaft and vigorously move up and down. When done, flick the pad against a chair or table to knock out the dust. It is cheap and makes the shaft very smooth. It will eventually (10-20 years or so of daily use) reduce a shaft's width.
Damp paper towel - this is good for a light level of dirt. Make sure to follow up with a dry paper towel to remove any moisture.
Rub with a pad soaked in alcohol, then seal with a pad lightly soaked with lighter fluid - do this at home where you can sit down and do a proper job.
Extra-fine 1000-grit sandpaper - cleans well without taking much wood away.
Micro-fiber towel - best used to clean the shaft when your hands are a little sweaty. When dirty, just throw in the laundry.
Brown paper bag - fold around the shaft and rub vigorously (seals wood pores with a waxy additive in the paper).
Dollar bill - fold around the shaft and rub vigorously (transfers the printed oil-based inks into the wood pores).
Pumice hand cleaner - use primarily to remove chalk that is embedded into a wooden shaft.
Commercial products - there are a number of shaft cleaners available that have a good reputation for doing the job.
Check among other regular shooters and try whatever they are using. Some individuals have reasons not to use one or more of these.
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