In many ways nut trees are similar to fruit trees (botanically speaking they are fruit) and their propagation, planting and care is pretty much the same. Probably the biggest difference is that most common nuts are produced on large forest trees and are too big for all but the largest gardens. Another difference is that most are wind pollinated.
Many nuts are high in protein and fats (nutrients lacking in many vegetable foods), as well as minerals, vitamins and anti-oxidants.
The large nut trees need a deep fertile soil for best growth (most are tap rooted) as they can get quite enormous given enough time. Some species take a while to start bearing, but don’t let this discourage you. Plant them and forget about them for a few years. Grafted trees start bearing a lot earlier than seedlings.
Most nut trees are tap rooted so give them a planting hole that is deep enough to accommodate the root. Don’t bend the taproot sideways to fit it in the hole.
Large nut trees should have a clear area underneath them so you can gather the fallen nuts (this is the only practical way to harvest them). Chestnuts create fairly dense shade anyway.
Nut trees respond to having nitrogen fixers around them even more than fruit trees.