Well.. your particular piece of outdated drive train is an O-ring sealed chain (or maybe Xring), so doesn't want for nearly as much attention as older standard chains did. It will also last a long time, maybe 20k miles, and won't need a grease repack like a shaft drive will.
There are many views on whether you should clean the chain or not.
Some say don't... I say it depends on what sort of dirt is on it.
I lube with either chain spray (grease) or gearbox oil. I don't use the chain waxes.
I brush the gearbox oil on it, or deliver it via a chain oiler I made.
I clean in several ways, sometimes by brushing on used engine oil then toweling off afterwards, sometimes I spray on WD40 and then towel off. I have used paraffin and even diesel to remove the old used up oil/grease before applying fresh lube.
Do not use water and detergent to clean the chain.
Do not pressure wash the chain.
Rule of thumb is 500 miles between clean and lube, and just lube in between as needed.
Chain oilers are great, especially if you do high mileage or are touring. No need to buy an expensive one, you can make one yourself for very little money that work just as well.
Manual lubing (and cleaning) depends on what conditions you ride in, in time you'll just get the feel for when it wants for something, be it a little oil or maybe a clean.