Wood is produced by esignating rees to be chopped down. Any dwarf with the wood cutting labor enabled and access to a battle axe will cut down the trees, which will turn one tree into one log, the raw form of wood.
"Timber" is the name of the ninth month of the dwarven calendar, covering late Fall.
Trees start their lives as saplings. Saplings cannot be cut down until they mature into full-grown trees, which can take several years. Saplings will randomly appear outdoors to provide a slow (but steady) supply of wood. Once you reach the cave river, any unsmoothed muddy tiles will spawn tower-cap mushrooms which can also be harvested for wood. Fully-grown trees will impede units' movement, so be sure to clear them out of active corridors.
Besides cutting down trees and tower caps, each wagon you start the game with can also be dismantled for three tower-cap logs. Wooden barrels and bins can also be obtained from the human and dwarven caravans wood whenever you buy booze/milk or cloth/leather from them. If supplies are especially scarce, additional logs can be acquired by allowing a human caravan's wagon to be destroyed, though this will anger them and may result in sieges.
Extensive woodcutting may anger visiting elves - after you get a baron, an elven diplomat will visit the fortress every year and request that you limit your woodcutting to 100 trees for the next year. If you accept a quota and then violate it, elven bowmen will likely take up positions in the wilderness and ambush any dwarves that happen to pass nearby.
 Reasons you need wood
- To build beds
- Without beds your dwarves will get unhappy thoughts from sleeping on the ground
- To build siege engines and ballista bolts
- These can be very effective defenses when traps fail
- To make enough charcoal to make your first bars of steel, required for making your first magma smelter and magma forge
- If you want obsidian short swords, they require one obsidian stone and one wood each (these swords likely consist of a thin wooden "paddle" with sharp flakes of obsidian forming sharp edges, like the Aztec macuahuitl).
- If you have access to obsidian, these can be a great source of quick weaponry early in the game, before any steel works are up to speed. Even on a tree-lite map, each weapon takes less wood to produce than a steel weapon (unless you have located the magma flow and sufficient amounts of bituminous coal).
 Reasons you want wood
- It is simpler to make items from wood.
- Wood can be burned to produce charcoal and ash, which are important ingredients in other tasks such as smelting ore, forging metal items, glass making, fertilizer for crops, and other uses.
 Reasons you don't need much wood
- Everything other than beds, obsidian shortswords, siege engine parts, and ballista bolts can be made without the use of wood.
- Once you've reached the magma flow then you don't need wood for fuel. If you have coal, you don't need (as much) wood to produce charcoal for steel. If you have both, you don't need wood to produce metal or steel products.
- If you plan your fortress accordingly, you can grow your own wood supply underground with tower-caps.