There really isn't all that much to it, yet some people still find themselves trapped by the side of the road because they don't know how to change a tire. It's a relatively simple job that requires very few tools, almost anyone can do it and once you learn how to change a tire you won't have to worry about hoping for the kindness of strangers to get you back on the road again. The key really lies in the preparation: make sure, at the minimum, your car is prepared with the following: Either a full size inflated spare tire or a temporary spare tire. A jack that fits your car and your owner's manual to tell you the proper placement of the jack to avoid damaging the frame of your car.
A lug wrench to loosen and tighten the lug nuts. And last but not least - a tire gauge. Things like a pump, in case your spare has gone flat or some WD-40 or other penetrating oil (for lug nuts that are difficult to break) can be good additions to your tire changing tool repertoire, but usually aren't as necessary as the above mentioned items. Now we'll get into the specifics of learning how to change a tire. First things first, you'll need to pull off of the road (preferably to a flat, level surface). Turn off the engine, put your car in park and apply the emergency break.
If you're on the shoulder or side of the road, still in proximity to the flow of traffic, you'll want to put on your hazard lights. Get your jack, the wrench, the spare tire and your owner's manual and make your way over to the flat. You may or may not have to remove a hub cap depending upon the wheel of your car, if you do the lug wrench usually has a flat blade opposite the head to pry away the cap.
While the car is still on the ground, begin to loosen the lug nuts by turning the wrench to the left, or counter clockwise. Unscrew the nuts until they are each loose enough to move by hand, but not quite until they are all the way off. Check your manual again to ensure proper placement of your jack and follow instructions for jacking the car high enough to give yourself room to work when removing and replacing the tire. Once the car is off the ground you can completely unscrew the lug nuts, I usually like to put them inside of the removed hub cap to ensure that I'll remember where they are when I need them again.
Take off your flat and replace it with your full size or temporary spare, then go to the removed hub cap and retrieve your lug nuts. Don't tighten any one lug nut all the way before addressing all of them; tighten them each a little bit at a time to ensure the tire is going on evenly. Once all of the lug nuts are relatively tight, the car can be lowered back to the ground - attempting to tighten them with absolutely all of your might while the car is still in the air can cause the jack to tip and result in serious injury. Once the car is safely back on the ground, you can work on securing the tire completely by putting some elbow grease into tightening the nuts again. If your psi (found by using you air pressure gauge) is lower than what is recommended (printed on the side of the tire), you can stop by a gas station, convenience store or anywhere with an air pump to fill it to the appropriate level. Now that you know how to change a tire, and know what you need to be prepared to do it, you can feel comfortable that you won't be inconvenienced that much or kept off the road for too long should the situation arise.
It's imperative to be prepared for any emergency when you're out on the road. Make sure you know how to change a tire, and it's also a good idea to belong to your local auto club.