Once the old wheel is off, place it flat on the ground and slide it under the edge of the car, leaving room for you to continue to work, of course. Now if the car falls off the jack the additional height of the wheel will lessen any damage. However, if the jack was placed on a flat, solid base and other precautions were taken, there should be no problems.
Now mount the spare tire on the wheel hub. The deep side of the spare should face the inside of the car. Take care to align the rim of the spare tire with the wheel bolts. Then hand tighten the lug nuts. Some lug nuts are open at both ends. If this is the case, the cone-shaped end goes in towards the rim -- the shape helps center and lock the nuts in position. With poor vehicle maintenance, sometimes the bolts may be too rusty to hand-tighten so start them by hand just to make sure they're not cross-threading, and then turn them on with the lug wrench until they're snug but not tight.
To ensure the nuts are snug and applying even pressure across the wheel, tighten them in a pattern where one nut is tightened, then move to the opposite nut. For a five-stud hub this equates to a star pattern. For four- and six-stud hubs this means tightened in opposite pairs, then moving the wrench one stud to the left or right and tightening that opposite pair until all the nuts are tight.
Because the car is up in the air at this point don't use too much force. The idea is to simply tighten the nuts enough so when the car is lowered the wheel won't pop off under the weight.
Remove the old tire from under the car and lower the vehicle until the wheel touches the ground, but isn't yet bearing the full weight. Now fully tighten the nuts in the same pattern you used before. Then lower the car all the way to the ground and remove the jack. Tighten the nuts one more time, as tight as you can make them without straining the wheel studs.
Stow your jack and tools in the correct place (remember this is part of good car maintenance) and put the old tire in the trunk or on the back seat. Your first order of business now is to have the flat tire repaired or replaced and mounted by a professional.
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