Clean off any obvious bits of debris and gunk and just spray something like Legia oil everywhere, I've never had to do the former whenever I've had mine apart and doing the latter has never hurt.
I'm sure there's a more appropriate set of oils and greases that a gunsmith would use if he'd stripped the various parts for a proper clean but a spray oil like Legia that doesn't hurt wood can't be too bad.
On Browning / Miroku , because it’s easy-peasy , you should also remove and clean the firing pins as well . The bores that that run through to the breach face often get clogged , and as the top pin does not have a return spring it’s common for them to stick . There are good videos of how to on YouTube .
I'm waiting to hear back from Fausti - Italy, to see if I can get instructions to my gun on how to strip.. Id love to take it apart and give it a good clean. I don't think its been touched since it was put together in 1996.
I give it a clean each time I use it, but have never taken the action out. I just don't want anything pinging across the room unexpectedly. This is a helpful thread - thanks for posting.