Assuming a skilled technician and cooperation of the subject, the best way to measure body fat is hydrostatic underwater weighing. Nearly as good and less expensive is DEXA (duel energy X-ray absorptiometry).
The least expensive is air displacement (BodPod) and it is nearly as good as underwater weighing.
As a practical matter at home, using plastic skinfold calipers may be all you need. They involve a one-time expense of $20. .