Three main ways to measure body fat are calipers, bio-impedence or hand held devices and hydrostatic testing. Hydrostatic testing can be done at universities or hospitals but are expensive.
Caliper and hand held devices are more common for most folks. Both have a margin of error of about 3-4%. Calipers are better if someone else take the measurements for you AND they are trained professionals. Caliper measurements need to be taken in at LEAST three areas (usually belly, thigh and triceps). Then average them all out and get an overall number.
Handheld devices are easy to do alone. It takes about 7 seconds for a reading to come back. The reading can vary depending on your body's hydration levels, sodium levels, temperature, and a host of other things.
Overall the actual number is not as important as the range you are in. You also want the overall pattern of your body fat % to decrease until you are at healthy levels.
Calipers and hand held devices will both give you an estimate to as to how much body fat you actually have.
Here are ranges of body fat levels:
For Women
Essential Fat= 10-12%
Athletes= 14-20%
Fitness= 21-24%
Acceptable= 25-31%
Obese= 32% plus
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For Men
Essential Fat= 2-4%
Athletes= 6-13%
Fitness= 14-17%
Acceptable= 18-25%
Obese= 25% plus
*These numbers are according to The American Council on Exercise