My preferred method of measuring body fat composition is Hydrostatic Weighing. Hydrostatic weighing, or underwater weighing, is considered the "Gold Standard" of body fat measurement that requires being submerged in a specialized tank of water.
It works mainly because bone and muscle are more dense than water, so a person with less fat will weigh more in the water and vice versa. The accuracy of the reading is contingent upon blowing all the air out of the lungs during pretest screening. The test takes about 20-30 minutes, costs around $100-$150, and is available at research labs, universities, or hospitals.
The advantage of this method is its accuracy, however it can be impractical, expensive, and difficult to repeat. This method produces a very accurate result, hence it is a lot more reliable than many other methods, if the user wishes to have a very clear idea of his/her body fat composition.