I remove anything that locks down, and use one of SWMBO's Hair curling brushes (that she never used), to clean out the inside of the die.
Followed by either some Diesel, on a cloth, or Lanox (a lanolin based lubricant), to polish the inside if I am reloading, and reassemble.
When finished I repeat the process, but use a little more Lanox, to prevent rusting, in storage.
Cheers
Bucky