Make sure you have a spare tire.
You'll need a spare tire obviously, always keep one in the trunk, or the back of your truck or SUV. You'll need a car jack, along with a tire iron. Keep these in your vehicle at all times.
Make sure you have the proper air in the spare tire.
You can get an air gauge to check on it. There's nothing worse than changing a flat tire, to find out the other one is flat too! Then you are totally screwed.
Make sure your vehicle in on a flat surface, not a slope.
This is important to avoid some kind of injury.
Use an object to put behind the tire opposite to the flat, to block it.
Use some extremely heavy object. That way when you jack the car up, it doesn't move backwards. Also make sure the gear is in park.
Take the tire iron, and loosen the lugs.
Right, tight. Left, loose. Don't remove the lugs. Just loosen them. Use some strength, they'll be on pretty tight. Maybe have some working gloves in the back car, for a tighter grip.
Remove the lugs once the flat tire is completely off the ground.
Don't lose the lugs, you'll need them.
Put the spare tire into the wheel studs.
Make sure the tire holes line up with the wheel stubs. Put your foot under the tire to maintain balance for the wheel, makes it a little easier. This step is the most difficult.
Use your own hands, take the lugs and screw them back on(right tight).
Once they're tight enough, use the tire iron to get them a bit tighter. Don't have to get them completely tight yet.
Lower the jack, remove it and put it in the back of the vehicle.
Take your tire iron and tighten the lugs again until they can't be tighten any further.
It's VERY important you make sure they're completely tight, with the tire back on the grown before you take off.
Get back in the car and slowly drive to make sure the tire is in place.
If it's all good, you're done.