This is going to seem complicated and obsessive - actually takes less time to do than it took to write this little "guide".
Cleaning with warm soapy water works nicely to remove the usual "stuff" that collects on mechs. Dry with compressed air (compressor or computer blast cans) or just soft cotton toweling. Some prefer to use nothing but 99% IPA... which I have no issues with if that's your preference.
If the contacts have a bit of corrosion, that can be
gently removed with a
fine scotchbrite pad, equally fine stainless steel wool or sponge - or 1000 grit or finer wet/dry sandpaper. Rinse cleaning residue with 99% IPA.
Although I prefer
MG Silver grease on electrical contacts
and even threads (link for tech reference - buy from Amazon - it's cheaper) - it can be a bit expensive for some - so what ever your preferred anti-corrosion electrical grease - Noalox, Ox-Gard, NO OX ID A and so on. Bare, clean SS works just peachy too.
If it's bare, polished SS, you may re-polish it with any common metal polish - Mother's, Simichrome, Nevr-Dull - what ever you like - to maintain the finish. Some polishes will leave a protective residue... which in most cases IMO, isn't all that protective.
Finish with a few light coats of (specifically)
Renaissance Micro-Crystalline Wax to all exterior surfaces (read up on this and you'll understand why it's preferred by so many) - work it in with your fingers then buff lightly to remove residue, using an "extra soft" toothbrush for grooves/crevices and engravings.
Make sure there is no water remaining inside prior to installing a battery.