It's vital that the bicycle you rely on is in good condition. Learn to do simple jobs like lubrication and brake and gear adjustment. Clean your bike regularly. Take your bike in for a service at your bike shop at least once a year. Essential safety critical parts that you should check often are:
Wheels: Are your tires in good condition and correctly inflated? Don't ride on bald or flat tires. Are the wheel bolts tight enough to hold the wheel in place? If you have quick-release wheels check that the quick release is correctly tightened every time you ride your bike. Does the wheel run straight and true? if there are wobbles in the spinning wheel your bike shop can easily "true" them for you.
Cables: Check all your brake and gear cables for signs of rust, wear or fraying. The brake cable is one of the most important parts on a bike so make sure you keep a close check on its condition. If your cables look worn out get your bike shop to fit new ones.
Brakes: Test the brakes before you get out on to the road. When looking at the brakes check that the brake pads are not worn out, and that they make contact with the wheel rim correctly when force is applied on the lever. Ask your bike shop to show you how to perform day to day adjustment on your brakes.