This question is on behalf of my father.
He planted a Walnut tree about 40 years ago and to this day it still produces healthy walnuts.

I don't know why, but he wants to cut it down and wants to know, is there a right way or a wrong way to cut the tree ?
The tree trunk is just over 4 feet high and about 18 inches in diameter, maybe more.
It has thick overgrowing branches.
He thinks furniture makers buy correctly cut Walnut Trees to make Walnut furniture.
If this is so, do Walnut Trees have a "value" ?

Thanks in advance,
Much appreciated

I doubt such a tree has much value as lumber. It would need to have a much higher trunk, and 18'' may be too small. Insist he finds a buyer before cutting it. Otherwise I am afraid it will end up as firewood. Maybe your county extension agent can tell you more.