Step 1: Things You Ought to Know
Rotating your tires regularly (yearly) ensures that they will wear at a similar rate, ensuring that your car handles like it should. A car with uneven tire wear may handle erratically, especially in poor road conditions, and can make emergency maneuvers unnecessarily dangerous.
Why shouldn't I rotate my car's tires?
In some cases, tire rotation is unnecessary or even inadvisable. If your tires are equally worn front and back, you probably don't need to bother. Also, if your car uses different-sized tires in the front and rear (common in high-end rear-wheel drive vehicles), tire rotation can drastically and negatively impact your car's handling.
Is there a pattern I should follow?
Yes. The pattern in which you rotate your tires is entirely dependent on which wheels are driven on your car. For a front-wheel-drive car, the front tires should move straight back, with the rears moving diagonally across the car. Rear-wheel drive is just the opposite. For 4-wheel and all-wheel drive vehicles, all four tires should move diagonally across the car. This ensures that tire wear is as consistent as possible, even if you tend to turn one direction more than the other.
The car used in the illustrations is front-wheel-drive.
Step 2: Things You'll Need
Your car most likely came with one of these. The owner's manual should tell you where it is located and how to access it.
Scissor Jack and Lug Wrench/Breaker Bar
If your car has a spare tire, it almost certainly has these. Again, consult your owner's manual for location/use.
Although this tool isn't technically necessary, I'd recommend using one anyway. It makes the removal of the lug nuts go faster, and also makes them harder to over-tighten. They are pretty cheap to buy, and even cheaper to borrow. The odds are pretty good that you know somebody who has one.
Step 3: Finding a Good Location
Step 4: Jacking the Car Up
Carefully raise the jack into the appropriate jacking point on the underside of the car (see your owner's manual for exact location of jacking point). After making sure that the jack is seated properly, continue lifting the car until the wheel is about 1 inch off of the ground. Remember, scissor jacks aren't the sturdiest things in the world, and cars are heavy. Please do be careful, and stay out from under the car at all times.
Step 5: Removing the Wheel
After all of the nuts have been removed, grip the wheel firmly with both hands and pull it off, jiggling it as necessary. This is easier if you are sitting down.
Step 6: Replacing the Wheel
Lower the car back down and remove the jack.
Step 7: Repeat
Congratulations! You are now the proud owner of a set of freshly-rotated tires.