The accuracy of these scales varies. The gold standard for bodyfat measurement is either a hydrostatic tank measurement, or more recently, by DEXA scanning. DEXA (dual energy X-ray absorptiometry). DEXA measures bone density, but also takes care of calculating body fat percentage.
This is a whole body scanner that can tell you where your fat is located – using a low dosage of Xray. This method is around 2-3% accurate and is considered the most accurate method.
It is more expensive than hydrostatic weighing. For hydrostatic weighing, you need to get weighed, with almost no air in your lungs, underwater. It uses the fact that fat is lighter than water, so you weigh less in water than in air. This also gets to aroun d 2-3% accuracy.
Calipers are another way to measure body fat, but they take a skilled practitioner to get a good level of accuracy.
Bioelectrical Impedance is the method used in body fat percentage scales. An electric signal will travel from hand to hand or foot to foot. A faster signal means more muscle – and this can be even 4-5% accurate.
If you are dehydrated though, the result will be less accurate.
BMI charts are a rough idea but I would say they are quite inaccurate for people further from the “normal” weight.