First step is to check your oil dip stick everytime you fill up with gas. This will ensure there is not an oil leak you may not be aware of. Change your oil every 3000 miles or sooner. Every month you want to check your coolant levels to make sure your engine is not over heating.
you should be checking your air filter monthly. This has to be the most underrated but important piece of your vehicle. If your air filter is dirty or clogged then your destroying your engine and gas mileage. It is vital to be checking it monthly. If it is dirty you can just remove it and wash it with water and it will work as good as new.
Next is to keep an eye on your tire pressure. With bald tires your gas mileage wont be as good. One classic way to check to see how much tread life you have left is to take a penny and turn it upside down. Abe's head will be upside down and you put the penny in between the tred on your tire and if the tread is lower than the top of abe's head then you are probably in line for some new tires.