From The Heroes of Might and Magic III wiki

Wood is one of the three basic resources in Heroes (along with Gold and Ore). Wood is needed for most buildings, and thus, it is vital to claim a source of Wood as early in the game as you can. The primary source of Wood is the Sawmill, which brings its owner 2 units of Wood per day. You can also find Wood scattered around the land in small amounts (5-10 units of Wood per resource stack).

In Fortress, Castle, Necropolis and Stronghold towns you can also build the Resource Silo which will bring you 1 Wood and 1 Ore per day. Any hero equipped with the Inexhaustible Cart of Lumber gives you 1 Wood every day.