The League of American Bicyclists suggests performing an "ABC Quick Check" on your bike before you ride. The acronym ABC Quick Check reminds riders to check for air in the tires, brakes that work, cranks and chains in place, quick release systems that release properly, and to check the overall bike before riding.
Bicycling magazine offers a three-point tutorial on bike maintenance, giving how-to tips for cleaning out a bike chain, adjusting brakes, and smoothing out the shifting on a bike.
When it comes to on-the-go maintenance and repairs, it is always helpful to bring the following with you on a ride: a spare tire tube, a flat-tire patch kit, tire lever, and a multi-tool with assorted screwdrivers.