In the absence of a specific problem leave the trigger where it is. Most people don't remove them. If maintenance is necessary then remove the stock and clean and lubricate the trigger with it still in place.
My usual over/under cleaning routine is after every outing to remove and replace the hinge grease, brush and swab the bores, wipe the metal with a lightly-oiled rag, clean the choke tube threads and lightly grease the choke tubes. To be perfectly honest if I'm shooting the gun on a weekly basis and it wasn't raining I might just replace the hinge grease and wipe the gun down. I will do the cleaning routine each time if the gun is one I don't shoot frequently.
Once a year I might take the gun down further, clean the ejectors, take the stock off just to see if everything is in order, check any of the various parts for wear. I do not do a full disassembly.