Let me frame my comments with this:
I had a Beretta 686 Silver Pigeon that I put (conservatively) 60,000 rounds through using this method and the jewelling on the side of the barrel-receiver mating surface was JUST starting to show the slightest arc of wear. After 60,000 rounds and probably 50,000 cycles total (including all the dry fire practice and misc. fitting/handling).
I used a red grease called "Shooter's Choice" which you can get most anywhere; it comes in a syringe with a white plastic applicator tip so you can really control where it goes.
Disassemble, wipe all the dirt and residue up (comes up nicely with this grease, without using solvent); quick dab (the size of about 1/2 of a peppercorn, say) on each of the pivot pins in the receiver and the female mating surfaces on the barrels. Lube the curve of the pivot, and the flat of the mating surface (so it spreads evenly by itself, without having to stick your fingers in it). Put the same small dab on the barrel mating surface (both sides), and give it an even smear with your clean/dry finger. Put a little dab on the locking lugs (if a Beretta-style action like mine was). Reassemble the gun and work it gently a few times. Before you put the forestock on, put the TINIEST little dab on the tip of the ejector plungers (the 'beak' that sits covered by the forestock) and smear it lightly with a finger.
If you disassemble the ejectors from time to time, as you should, then clean the channels well and lube liberally - can't have too much in THERE, unless you're shooting in the butt-cold... in which case, take a swipe of low-weight synthetic motor oil and put it on cleaned-to-the-bone parts there.
Voilà! You wouldn't believe how good the wear protection is with SC grease, IMO.
-M