If there are two things you need to maintain on your bike they are the tires and the chain:
Tires need air. Most pumps have gauges and generally your tires will tell you what pressure they should be inflated to. You should check this before every ride. Proper tire inflation will ensure a smooth ride and reduce the potential for a flat.
The chain needs to be cleaned and lubricated. Regularly. Compared to bearings in your wheels or the bottom bracket your chain is open to the world and all of its dirt. The chain is also one of the most used part of the bike as it is in motion whenever the pedals are moving. Finally it is made up of a lot of parts that are rubbing together causing friction and wear. Here is a nice overview of how to clean and maintain your drivetrain:
Long ride today, about 2 hours with some technical work. I opted for a new route that I have thought about doing a lot. Taking a right out of my driveway I went about 3.3 miles and took a left onto County Road 40. This climbs steadily to a trail system called Chicken Creek which crosses over to County Road 41. CR41 goes way up into the San Juan National Forest, which is what I did. The weather was perfect and I didn’t see any vehicles driving until I turned around and was descending.
I am at a loss for words how great this ride was. I felt like I could have just kept riding all day. If I had not made a commitment to help a friend I would have just kept going till I hit snow.
I will probably take the same route tomorrow and see if I can link up to Road 561 and come back into town by Jackson Lake Reservoir.