In the boot of the car there should be:

• A tyre wrench (cross - shaped spanner)
• A jack
• usually a separate thing to turn the jack with
• a spare tyre, with the right air pressure.

• a car owner's manual

• Decide you should have done a trial run at home, so you would know where everything is and be sure you have everything, and could do it for the first time in peace and relative comfort.
• Park the car, putting the handbrake on and putting it in gear or in P (automatic gearbox). This stops it running away. Find a couple of large stones to chock the wheels with, just to be doubly sure.
• Locate all the tools and manuals and stuff.
• In the car owner's manual, locate the safe-points for lifting the car body.
• When you fail to find the car owner's manual, lie down beside the flat tyre and look for little notches in the chassis. They're like the notches you put in the seam allowance when sewing, to match one pattern piece to the next. That's the safe-point. You can get up now.

  NOTE: I've been told that some cars have nuts that lock. Some cars may have other peculiarities. If these instructions don't match your car, you may have an unusual car. You will need the owner's manual to help you figure out what to do.

• If the hub cap is preventing you from seeing the nuts on the flat wheel, remove the hub cap.
• WHILE THE WHEEL IS ON THE GROUND, loosen the four nuts holding the flat wheel on. Just loosen them enough that they can be taken off later. If you have trouble, 'step on' the tyre wrench- use your leg muscles.
• Get out the jack. Put the jack under the car. There should be a flat bit for sitting on the ground, and a funny-shaped bit opposite for 'gripping' the car at the safe lifting point. Try to locate the jack so that it's directly under the safe lifting point.
• Put the turny-lever into the jack, and start turning. Turny-levers fit differently on different jacks - it's a good idea to do a dry run of this when you first get the car so you have plenty time to figure out how yours works.
• Adjust the location of the jack so it really IS holding the car by the safe point, and by the bit of the jack that's designed to.
• Lift this corner of the car just enough so that the flat tire clears the ground. Don't try lifting it too high, you're going to have to lift the new wheel however high you lift the car.

  WARNING: the jacks are not rated for holding a car above a human being. Keep any parts of yourself that you value out from underneath while the jack is holding the car up. Put the new wheel flat on the ground under the sill (bottom of the doors). Yes, ideally you should have used an axle stand, but how many people carry one of those around? Honestly?

• Finish unscrewing the nuts holding the flat wheel on.
• Pull the flat wheel outwards, off the bolts. Swear when you drop it on your toes. Promise yourself never to do THAT again.
• Swap the flat for the new tyre (spare). 
• Lift the spare onto the four bolts.
• Discover that you don't quite have enough clearance to get the spare on. Jack the car up a little more. Lift the spare onto the four bolts, for real this time.
• Tighten the nuts almost all the way.
• Lower the jack, till the spare is firmly on the ground.
• TIGHTEN THE NUTS ON THE SPARE. I forgot this step once, nearly lost the spare, and stripped the wheel nuts. Doublecheck that the nuts are really tight. (It doesn't hurt to 'step on' the tyre wrench to make sure they're tight!)
• Put the jack away. Put the car manual away. Put the turny-thing away. Put the tyre wrench away.
• Get in the car. Have a feeling you forgot something.
• Get out of the car. Pick up the flat wheel. Put it in the boot.
• Get back in the car. Stare at your filthy hands. Find something to wipe them off with. Promise yourself to get rubber gloves and/or hand-wipes next time you're at the shops.
• Drive off.

• Take the flat wheel to a tyre-repair place. The VERY NEXT business day. Or the same one. As soon as possible.