Some of the items can be checked by yourself like your tires. It is a good idea to check the tire pressure of all 4 tires at least once a month. And visually inspect them for loss of air, tread depth, balding and improper tread wear, bubbles (these can be quite dangerous and result in a blowout on the road), etc… Proper tire inflation will also help you get better gas milage (this is why some shops are now offering nitrogen for filling tires as it keeps the required pressure better).
Along with your tires you can change your oil, fluid levels, check your air filter (hopefully you already do this on a regular basis), etc… Many items like tune ups, brakes, serpentine belts, a/c system, radiator hoses, etc… require specialized equipment and basic to advanced automotive knowledge and may be best left to a mechanic and your local repair shop.
