I check the chain before every rid to check it's clean and lubricated.
Each fortnight or so - I will look for wear and tight links by turning the pedals slightly backwards and looking at each link for dirt and tight links
Each month I give a quick cleans. - lots of newspaper. Like the Mad Doc - read lots of papers

( He is addicted to local press though

)
I use a good chain cleaner and all bike shops sell them

and I uses a toothbrush and a solvent with a cloth to wipe the chainings of excess water after cleaning
I then use a lubricant from my local bike shop which is designed for bike chains - GT85 like my mate ed-m

and wipe off excess lube..
I also checkl for loose cranks and cahinaings for damage or for loose bolts.
Every two months of=r so - I fully remove the chain and give it a darned thourough clean with a toothbrush. - solad it overnigh in "fewnwicks" and dry with a clean cloth. Then I lubricate and refit to bike. I do check for chai stetch as well.
After all - no chain - no cadence- no speed - no thill and well maintained chain means smooth and decent ride
