And how do I know what to DO? And what to do first? Is there a checklist or an order of work or something to service a bike?
Maintenance is ongoing with bikes. I find that I need a new chain every 3,000 miles, tires can last 7,000 miles, etc.
If the bike is really old and hasn't been maintained, I would start with this list:
1) Check to see if you need a new chain and cassette, and possibly chainrings -
https://www.sheldonbrown.com/chain-wear.html2) Check your brake pads to see how worn they are, and replace if necessary.
3) Check the cables (brakes and shifters) - if they're fraying and/or rusty, time for new ones. If they look rusty, the cable housings should probably be changed out too.
4) Cranks and pedals - unless you hear a lot of squeaking, grinding, or clicking from the bottom bracket (where the cranks are attached), I'd just leave these alone and make sure everything is oiled and moving smoothly.
5) Tires/tubes - tires can develop cracks when they get old. If they are in really bad shape, it's probably time for new ones. Tubes are cheap, so if they are old, i'd replace those too.
6) Headset. Go down to the troubleshooting section of this link and see if you have any of these issues.
https://www.sheldonbrown.com/headsets.htmlIf you have any bike shops close to you, ask them if they do any classes on bike maintenance. Two of my local bike stores offer classes that are great for beginners. One store had you bring your own bike and work on it, and the second store just worked on one bike with the group watching what they did.