Lubricate all moving parts at pivot points, with a single drop of good oil, like "Chain L". Wipe off any you can see with a rag. Clean the frame with any car wax, and wipe shiny . Fenders help keep you and the bike much cleaner, and make it less maintenance intensive.
Just keep it clean, oiled where needed, and just ride it.
Typical, good quality hybrid with aluminum frame and stainless steel components and parts don't need too much attention, unless you ride in wet or snowy conditions.
I haven't had my bike for too long, but I've cleaned the chain once and re-oiled using White lightning Epic Ride chain lube. Using just a cheap toothbrush I knocked off whatever dirt/grime was on the chain in combination with a biodegradable citrus degreaser (Mean Green). For cleaning the frame I used diluted soap in water wiping with a sponge. Then using light water pressure just rinse the bike off keeping away from seals directly. Afterwords I just dried using some cheap wash-clothes I picked up from the dollar tree(also picked up a biodegradable degreaser there as well). I should note the only reason why I cleaned the frame so thoroughly is because I ran into a lot of mud under a bridge(nearly wiped out too).