Number one thing if you are stuck on the side of the road make sure you are as far off the road way as possible. Number two is to block the tires with chucks or large rocks to prevent the car from rolling off the jack. Number three places out safety cones or flares in front of and behind your car. This will help passing motorists see you, giving them enough time to pass you safely. The only other safety tip I can suggest is to please be safe while using a jack. Make sure it is placed in a safe place to lift the car and to always lower it slowly preventing you or the car anymore damage. Always check your air pressure in the spare tire before driving off. If it is low get air into it as soon as you can. Plus I would say after another 100 miles of driving on the tire it is good to recheck the air pressure and to make sure the lug nuts are still good and snug.
Removing the flat tire
The first thing you will need to do is loosen the lug nuts on the flat tire. You can use either the four way wrench (usually located in the trunk with the jack) or a socket wrench with a breaker bar. If the lug nuts are covered up the cover can be either pried off or removed with a special key provided with the car. I usually keep my key in the glove box. Then the next step is to jack the car up so the tire is lifted of the ground. Most cars are equipped with jack located in the trunk and there are marked areas on the frame of the car where you can place the jack so it is safe to use. I use my own hydraulic jack which I find a lot easier and faster. After the car is safely raised up you can finish removing the lug nuts and place them in a safe place so they don’t get lost or scattered around. Now you are ready to remove the tire. Lifting up on the tire and pulling it towards you should work but if the tire is stubborn you may have to rock it back and forth to break it loose. After you have removed the tire place it safely out of the way or in the trunk of your vehicle or wherever the spare tire is located.
Mounting the good tire
I find it easiest to place the good tire on the ground just in front of the lugs and then sitting on the ground just in front of it with my legs startling both sides. If you have some lube handy, it might be a good idea to coat the lugs with it. This will help make the nuts easier to remove the next time you have to change or rotate your tires. Then I line the holes on the rim of tire up with the lugs and lift up the tire and slide it on the lugs. Now while holding the tire flat up against the wheel you can start the lug nuts back on their posts hand tightening them until you has all of them on. Now you can use your four way or socket wrench to tighten them almost all the way. Start with the nut at the top and then tighten the one opposite working your way around the tire so that the tire is mounted evenly. After you’re done with this you may lower the car down off the jack slowly. Then you can tighten the lugs firmly. I would go about a quarter of a turn past snug.