There are three ways to measure body fat.
1)Home Body Fat Scales
2)Skinfold Calipers (Calipers)
Home Body Fat Scales are not much expensive, you can get a good one for 30 $. Here a low level electrical current is passed through your body, which uses The bioelectrical Impedance Analysis (BIA) to find the body fat percentage. This method is easy to use, but many cases it will not give you precise results.
Bioelectrical Impedance depends on body temperature, present water consumption of your body, or even on the recent physical activities. If you take few precautions like not taking too much water before the test (I meant 3/4 hours here) and not doing excessive physical activities before you take the test. Meaning don't take the measurement after finishing 30 minutes of running. Use the scale before you do any physical exercise.
Health O Meter body fat scale
Skinfold Calipersis an easy method to calculate you body fat percentage. You have to buy a calipers though. A calipers is not much expensive, you can get a basic one for 25 $. Getting the correct measurement is very important though. You can take help of a professional for taking the measurement, to get the best result in this method. If you can buy Accumeasure Calipers (a little bit expensive) then you can take the measurement yourself. Accumeasure gives best measurement.
Hydrostatic Weighing method is the most accurate one to measure body fat percentage. But here you need a Hydrostatic Weighing Pond. Fitness centers, Gymnasium or University sports facility can have a weighing tank like this. Here using the Archimedes principle amount of body fat is calculated. Here you will sit on a chair in the Hydrostatic Weighing Pond, the water you displaced will be calculated and then using the Archimedes principle body fat will be calculated. Though it is a very reliable method to calculate the body fat percentage, Hydrostatic Weighing Pond is not easy to get, so you may not always get the chance to use this method.
Another easy way is to use the Body fat percentage calculator available in different websites. Most of them are based on two methods, 1) A formula used by US Navy, and 2) YMCA formula.
US Navy method identifies amount of body fat from the measurement of your weight, waist, neck and abdomen. YMCA formula calculates from only your weight and waist measurement.
These methods are easy to use, just take the tape measurement of those parts as mentioned in the previous paragraph and then use one of the formula to find out the body fat percentage. Easy and cheap, since you need only a tape here. But these formulas are sometimes, specially for those who has a athletic body, not very accurate. Still you can have some idea. If your measurements shows you have 15% body fat, you can assume that actually you may have from 13% to 19% of fat.