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as far as the caliper way to do it, you measure in at least 3 different places - belly, elbow/forarm, and somewhere else, and there is a chart that has the thickness, the area, and the body fat % for that area, then you do a little quick math and get your answer
careful though, if your below 5% or so (like I am) then results become inconclusive, but overall it works as an estimate. The electronic scales are more accurate, claiming within a fraction of a percent in some cases. They work by treating your body as a resistor in an electric circuit and measuring your resistance, because fat conducts electricity differently than muscle, bone, etc. By combining this info with your height, sex and age, it can give you a good idea of what your percentage is.
I used to work at performance bike shops and I know we had some on display there for people to try out, so you can find out by just calling a sports shop and asking if they have one, and if you can test it (then claim that its calibrated wrong because you swear you are (x-10)% body fat :P )
hope that helps
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