Walnut Saplings are a nut bearing tree that reproduce Walnuts.
1.9.4 and Newer: Combine Three (3) Walnuts and ANY Sapling.
1.7.10 and older: Combine one (1) Walnut with an Oak Sapling
Plant the sapling as normal. When the nut has ripened right-click to harvest the Walnut. Do not left-click as it will permanently break the nut.
Bonemeal can be used to ripen the nut and grow the sapling into a tree.