A
jack stand is a
vital piece of
equipment when working under your
car. Believe it or not, the
scissor jack that came with your car is not very
stable and will not hold it up for very long. A
jack stand is a stand rated for a specific
load that can be placed under your car to hold it up after you have
jacked it up. It looks somewhat like this:
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The stand is placed under a frame rail or axle after the car has been raised and is adjusted to the right height either by a removable pin through a set of holes (this kind has a hollow tubular raising rod and is generally rated for less weight) or by a teeth-and-catch mechanism on the side of the rod (this kind tends to be cast steel and rated for more weight). When buying a jack stand, buy the one with the largest base that will fit under your car (larger base = more stable).
The other type of jack stand is a ramp, which is much more stable but not suitable for work requiring wheel removal. You pretty much place one ramp in front of each wheel and drive up on it. Very easy to use.
The surface on which you place your stand is critical: asphalt looks stable but the jack stand could easily sink into it, especially on a hot day. If one stand sinks in, it destablizes the entire set-up, making it pretty likely that the car will come crashing down. The best surface on which to place the jack stand is flat, level cement. On any other surface, you will need to add a stable floor between the jack stand and the surface. The easiest safe type of floor is a piece of wood at least 1/2 inch thick. Make sure it extends atleast 6in out horizontally from each end of the jack stand; surface area is crucial. If you are on any sort of grade, the best idea is to tie the uphill end of the car to a stationary tie point (tautly!). And make sure your parking brake is on.
Finally, never, ever use something else in place of a jack stand unless you know exactly how much weight it can take: cinder blocks crumble, stacked up wood tends to become unstacked (yes, even under pressure), and so on. Safety is crucial.