Depending on the condition of the dies is a factor on cleaning for me . Light rust I use 0000 steel wool&gun oil. Depending on the amount of sizing wax build up some CLP & q - tips or just put them away till next time. It’s basically your decision .
I’m kinda annal about it myself.
Upon a finished reloading session of a specific caliber, that die set and/or toolhead will be disassembled and cleaned with 99% alcohol and nylon brushes.
On the progressive it’s the same thing just take it a little further and include the bullet feeder and powder drop assembly. Coat the clean dies and exposed metal surfaces with Corrosion X. Have never seen a hint of rust on a die or a firearm.
First, I try to use reasonably clean brass. That cuts down on the amount of crud in the dies. I will do a thorough clean on dies with Ballistol after use so that they're ready when I need them again. During reloading, if I see there's some buildup of soot or brass filings, I'll use a little gun scrubber or brake cleaner on a cleaning patch to clean out the affected die.
I only clean when they start feeling sticky or gritty. Maybe 3 times in about 40 years. Disassemble clean with simple green wipe dry, lube threads if you are constantly messing with them Mine stay put and locked down. Each set has 2 dummy rounds for seating depth reference.
I disassemble and spray brake cleaner, then twist a paper towel tight, spray a little more brake cleaner on it, and push it as far up into the die, and then down through the top threads, as I can, still twisting as I go. I'll repeat using a dry paper towel.
If I'm gonna store the die afterwards, I'll often dampen a cotton patch with Hoppes #9 and run it through.
Bore brush plus whatever solvent you like for hard stuff. Scrub until you are happy and then clean up with air and some alcohol. For bullet lube, scrape first! A little CLP afterwards to keep the rust at bay on dies that need that and where you care about such a thing.