Generally...
I avoid licking, chewing on, seasoning, barbecuing, dunking in the toilet, or sweating on my dies. Seems to help.
I try not to use any solvent that will fully strip oil from the outside of the die. But, if I do, I re-oil with my preferred gun oil. (FP-10)
The inside of dies is pretty much ignored in my reloading room, after the initial cleaning -- at least in regards to corrosion prevention.
I wipe excess oil out of expanding and seating die bodies when new, and clean expanders and seating stems. (One-piece expander dies being a notable exception. Those get thoroughly cleaned and then a
very light coating of oil on everything but the expander.)
Sizing dies get a better cleaning, but not until they're going to be used.
Otherwise, the inside of the dies only get attention when I need to clean excess lube. -- And that's all I clean out:
excess lube.
It's far from textbook. ...But it works for me.
Oh, it may be worth noting: When not in use, the majority of my dies are stored in their original boxes, inside a file cabinet. Temperature and humidity are fairly constant, and there are probably six dozen corrosion inhibitor squares inside, due to the various tools or die boxes that still have them.
Is that what those little cardboard squares are that comes in the box of dies (hornady ones at least)??? Some kind of rust preventive soaked into the little square?
Yes.
They're VCI (Vapor Corrosion Inhibitor) emitters, generally good for a couple months, to a couple years in an enclosed space.
I always keep them - at least until I open the die box one day and think, "these dies are eighteen years old ... that was toast fifteen years ago."
When I buy tools that have the VCI disks, squares, or pellets, I toss the emitter(s) in with my ferrous reloading tools and throw away the old emitter(s).