The question as stated is very broad and a complete answer to your question would be very, very long! I'll endeavor to provide something useful in an answer of reasonable length.
Your best approach is:
1) Clean the bike thoroughly (kinda optional but it makes everything else easier and more pleasant). There are many videos and web articles on this subject.
2) Make sure the bike is safe and check for any obvious problems. Again, there are many videos and web articles on this subject, but I'll give a basic checklist. In regard to cosmetic vs. real damage: if there is anything that you are in doubt about, post a specific question on this site with a good description and photos or go to a good bike repair shop to get the issue addressed.
3) Deal with items that show wear or become maladjusted the quickest.
4) Start learning bike repair and maintenance to deal with everything else. There are many great resources available: books, YouTube instruction and how-to videos, and web pages. My personal favorites are the videos and web articles produced by Park Tool and Global Cycling Network.
For brevity I won't go into lots of detail below. Look for questions and answers on this site or Google for articles or instruction videos.
- No dents or damage to frame or forks, fork legs aligned
- No damage to any components; scuffs, scrapes or worn paint or finish is OK
- Brakes functioning and adjusted properly, brake pads not worn out
- Tires inflated to pressure in recommended range, not obvious damage to tread or sidewalls
- Gear shifting working OK, chain not slipping over sprockets, chain does not fall off sprockets when shifting
- Wheel rims run reasonable true, no dents in rim walls, no loose spokes
- Wheels, cranks, pedals spin freely
- No excessive play in wheel hub bearings, bottom bracket bearings, pedal spindle bearings
- Handlebars turn freely
- Headset bearings not loose
- Seat, seatpost, stem, handlebars, brakelevers, gearshifters. forklegs etc. not loose; generally all bolts and fasteners checked for tightness
- No excessive wear in chain, cassette, chainrings, chain cleaned and lubed appropriately
- Suspension forks air pressure set correctly, suspension works correctly and has full movement, no oil or fluid leaks
- Handlebars aligned with front wheel
- No fraying or obvious wear in brake or gear shifter cables, no kinks or cuts in housings, housings inserted in stops properly
Major wear items
Obviously everything wears out eventually but the primary wear items are:
- Brake pads
- Chain (chains wear before cassettes and chainrings, but a worn chain wears cassettes and chainrings out faster.)
- Cables and housings - they don't really wear as such but get contaminated with dirt which increases friction leading to spongy brakes and impaired shifting
Primary adjustment items
It's basically: brakes and gear shifting, but if you are riding the bike everyday you will want to go over the safety checks every couple of months at least to catch any issues before they become major problems.