Read your car owner's manual, it has every piece of information on car maintenance as well as safety precautions. It is the best reference guide for everyone who owns a car.
Keep all the fluids (e.g. engine oil, transmission fluid, coolant, etc.) clean and topped up. Checking the fluids often helps safeguard against breakdown, mechanical damage, and also possible accidents.
Comply with your maintenance schedule, there is a number of things that need to be regularly serviced or replaced at certain intervals for instance brakes, air filter, timing belt, spark plugs, etc.
Check tire pressure regularly. Your car's tires are made from rubber and are inflated with air. The air pressure inside the tire ought to be checked regularly to ensure safe and fuel-efficient operation of your vehicle.
Change your windshield wipers if they don't clean properly.
Wash and wax your vehicle once in a while to keep the car finish shiny and protected from corrosion.
Take care of any problems as soon as they arise, before they become more serious and require expensive repairs.
Only use original parts. Sure, you can save a couple of dollars now and get the part in the unmarked white box from the discount auto shop up the street. But you might be back into the auto shop sooner than later, and if your vehicle has a warranty, it could be affected by using an aftermarket part.
At least once a year have your car check out in a garage.