Now I'm riding less, I find I don't need to do as much except keep the chain clean and tires inflated. I still check cables, chain slack, and stuff but they tend to need less work now.
- Keep your chain clean. Every few weeks use a degreaser to clean it, wash it out with water and apply lubricant suitable to your weather conditions afterwards. There's a chain cleaning tool from Park Tools which makes the degreasing part particularly easy. I highly recommend it.
- Replace the chain every year. Chains will stretch and wear out the cogs on your cassette thereby deteriorating the whole drive train. There are distance recommendations and ways to mesure if it's time to replace the chain if you want to look them up, but doing it every year shoudl be on the safe side
- Replace your tires once they are worn out. I drive Continental Grand prix which come with a handy indicator on the tire itself, but you should be able to look up the recommended life span for your particular tyre
- Keep your bike clean. Cleaning your chain should be a welcome opportunity to also quickly clean the rest of your bike - doesn't have to take longer than a few minutes.
But many people have old bikes with rusty brakes, non-working gearing, and just go on using them until they fall apart.
Also, different bikes require different levels of maintenance. And your riding style and frequency of use affects the speed of wear.