"Shotgun Technicana" by McIntosh and Trevallion ("Crossedchisels" here) is an excellent read on the titled subject, altho it isn't just on gun care.
The most important specifics for a fine sidelock (in addition to good gun cleaning basics) that come to mind are:
1) Avoiding oil seeping into the stock head, where the wood endures high mechanical loads during recoil. Don't store with muzzle higher than breech end of barrels, and don't over-oil the locks.
2) Cleaning and lubricating locks should be approached thoughtfully. The book I cited describes important precautions to avoid chipping finely inletted wood surfaces. It's good to know how to get lockplates off properly, safely, if you ever have the gun in a soaking rain.
3) I prefer to store with locks uncocked (some others don't bother). If it's an LC Smith you probably want to ignore this because you have to re-cock with a tool or wrench before it can be reassembled. For other guns, firing with snap caps in the chambers, then removing forend and barrels gets this done easily.
4) Altho not sidelock specific, I always wipe off, and replace the thin film of grease on the hingepin and mating lump surface, using high pressure grease (Anderol is one). Reason is that dirt can be very abrasive and you don't want wear on those parts. "It's the film that counts."
