The discovery of a flat tyre on your car is best made as it sits in the garage. This scenario means that you're generally provided with a good surface on which to sit the jack. If, however, a strange 'helicoptering' flap-flapping sound is emanating from beneath the car while it is in motion, the driver can be in one of many degrees of trouble, depending where the car is.
One of the worst places is probably in a street with not a single parking space available, particularly if the street runs up a hill. There are other horrifying sites of course. A rutted gravel country lane with narrow or no verges comes to mind. And then there is, of course, a busy highway with the rain pouring down, in which case it would be best to call a professional from an automobile association who would have the right warning equipment, as well as the means to change a tyre quickly.
When stopping, allow the car to coast slowly to a stop if you can. Avoid slamming on the brakes or yanking the steering wheel as this could be dangerous.
Assuming that you are relatively safe1 and you've found a place to pull over and stop, what then?
Put your hazard lights on on, make sure the handbrake is on fully and put the car into first gear or park (this is especially important when changing a rear tyre on a front wheel drive car since the handbrake only locks the rear wheels2) and turn the engine off. Get out of the car and kick the tyre. This does not do much good except to relieve your frustration in a minor way. Put out a warning triangle if you have one (in some countries this is compulsory).
Placing a block on the opposite wheel is a very good idea. A brick, rock or log will work in a pinch.
Open the boot and find to your further frustration that you have to unpack shopping, luggage or general detritus that sits on top of the spare tyre and the jack before they can become useful. While there, check that you actually have a spare tyre in the boot, and that it is inflated before doing anything else.
Take the wheel trim or hubcap off the tire that is flat if there is one. The jack may have a flat end to help you, but if not a screwdriver will work if you have one. Loosen all of the wheelnuts, but don't undo them at this stage.
Since the wheel was most likely last put on in a garage, it will indubitably have been fastened with an electric drill attachment and so be will be beyond the strength of the average Hercules to loosen3. Calling upon all reserves of strength or the assistance of some passing Samson, the nuts may finally yield, though at the cost of knuckle skin. Remember that they undo to the left, although sometimes a little twist to the right first can help the really tight ones. You can stand on the wheelbrace to help move them if you need to.
Ensure that you find all the pieces of the jack. No doubt the winder will be as far removed from the body of the jack as is possible in the confines of your boot. If you are lucky the jack will still have the instructions printed on it.
Now jacks come in many shapes and sizes. Nowadays, the commonest one to be found in the average family car is that one which has the misnomer 'lady's jack', so called because some male chauvinist idiot believed that the fairer, more tender sex would have no difficulty in manipulating it, whereas in fact using it is a real problem to the most hairy-chested of males.
Inevitably it is already wound to its highest extension and has rusted in that position so that it cannot be fitted in the space between the ground and the car chassis.
Why was it not kept greased? You didn't think you'd need it. Bashing it on the ground may help to use up any excess adrenalin thus far accumulated and may even loosen it to such an extent that it can be placed in position.
Placing it is not always simple. The head of the jack must be carefully inserted into the correct point of the chassis and its foot set on a firm base which may even have to be constructed. A couple of pieces of strong flat wood kept in the boot is advisable for when this situation arises.
The correct jacking point can be found in the manual of the car, but to find the exact spot on the chassis requires kneeling in the dirt and running the fingers along the underside of the car, thus accumulating a thick layer of dust, oil and other unmentionable substances. If you really cannot find it, look for a solid piece of the chassis to use as a jacking point.
Make sure you have already loosened the wheelnuts, but that they are still done up before you jack the car up. The danger of pushing the car off a jack while trying to loosen wheelnuts is a very real one4.
Now jack the car up so that the flat tyre is completely off the ground.
Optional, but a good idea; if you've got steel wheels (rather than shiny posh ones) remove the spare from the boot and slide it under the car sill near the wheel being removed, so that should the jack slip when the flat tyre has been removed, the car will fall onto the spare. This could reduce damage to the car and prevent yourself from being crushed. Likewise when fitting the spare, slide the flat tyre under the car.
Undo the wheelnuts and remove them. Don't put them on the ground as they may get lost, tuck them into a pocket or put them in the car. The tyre is then removed from the uncovered bolts, and the hands made even filthier by the dust and dirt adhering to it. The hands are now only slightly dirtier than the knees of the trousers where the repairer had to kneel in the road dust.
The spare is removed from the boot and the driver may bless the fact that the last time he checked pressures, he or she inflated the spare as well. The wheel and hub must be secure and lined up properly before the weight of the car is put back on the spare. The centre of the rim where it mates to the hub is the most important since that is where the force is delivered from bumps and the rotational balance is set. Once the wheel is manoeuvred onto the bolts and held there with one hand, while then begins the frantic search for the nuts, which should have been placed together in the upturned wheel trim, but were not.
Found, they are finger-tightened into position, starting with the top one, until the wheel begins to spin.
The jack is lowered and removed, and the nuts fully tightened in a diagonal pattern while the wheel is firmly grounded. If you have five nuts do every other one until they are all done up. Put the wheel trim back on.
All that remains is to put the flat tyre in the boot, repack the shopping/luggage, replace the jack and drive off, leaving the wheelbrace on the verge where it had rolled under the car.
All in all a job best left to an automobile association mechanic.
If you have an 'emergency' spare (ie it would ruin the look of the car to put in a full-sized on, so you've got a piddly thin one) you need to go straight to a garage to get your tyre replaced and your original wheel put back on. Get your flat tyre repaired as soon as you can.