General Car Care
Oil Changes
It is typically good practice to change your oil every 3,000 miles. If you don't keep track of your miles very well, know that this is typically every 3 months depending on your commute and car use. My recommendation is to have a mini memo book to keep track of miles and dates of oil changes and all major repairs. This will give you a good idea on how much it costs you in upkeep of your car, and lets you keep track of when the next oil change needs to be.
Always go by the manufacturer recommendation for oil and filter type, and make sure that you change your oil regularly. This does NOT mean you simply top it off every few months. Change it. If you don't know how to, take it somewhere and learn, or learn from a friend. Procedures are generally the same for each car, and I will post basics for an Oil Change some time in the future.
Dead Headlights
Headlight Replacement Rule: Always replace in pairs, even if the other light isn't out yet.
Typically, when one headlight goes out, the other is not far behind. Avoid being left half in the dark a few days later (and avoid a possible ticket!) and replace both right and left lights at the same time. This goes for regular and bright headlights, turn signal lights, and all tail lights.
Tire Care
First of all, if it snows where you live, buy a set of WINTER TIRES. Yes, this costs a bit of money, but it could avoid a costly (or even deadly) accident. "All-Weather Tires" are not at all sufficient for snow. Trust me.
Secondly, rotate your tires on a regular basis. A good marker for it is every second oil change. This is something you can do yourself. The only thing you need to check is whether the tire is directional or not. Typically, if a tire is made to spin only one way, there will be an arrow and the word ROTATION>>> on it to let you know what side of the car it has to go on. Be sure to stick to that guideline.
If they require a specific rotation, then switch the front to the back, and vise versa. On a car with bi-directional tires, do the same, but then switch the left and right sides as well. This will help guarantee even wear on all 4 tires, and will prolong the life of your tires as well as providing a safer ride.
Thirdly, maintain proper inflation, and check for this regularly (once a month at least). A good habit is to check at the beginning of every month, and be sure the pressures in the tires match what is recommended in the driver's manual.
Wash and Wax Your Car
Wash your car regularly and be sure to wax your car at least once a year (preferably twice). Although it is convenient to take it to an automatic car wash, the power washers used can actually do some damage to your paint, grinding in dirt that does not wash away easily. Of course, doing this process the right way requires some practice and know-how. I'm currently learning how to perfect my technique as well. I recommend shopping around the web for good guides on how to properly wash and care for your car.