A wood furnace is used to convert wood into ash or charcoal. It must be built out of fire-safe materials.
Operating a wood furnace requires the wood burning labor enabled.
Building a wood furnace requires the architecture skill and a skill relevant to the material used to make the furnace (masonry for stone or glass or any of the metalworking skills for metal).
Wood is not an option as building material for this workshop, as it is not a fire-safe material.
Charcoal and coke, not very intuitively, are valid materials for building furnaces, since their ignition point is above the cutoff for fire safety. Soap made from dragon tallow is also an acceptable material. These somewhat more esoteric materials all use the masonry skill to finish the construction.
As with all other buildings that require an architect, Dwarves will admire wood furnaces and receive a good thought, its strength dependent on the overall value of the building, which is determined by the value of the materials and the quality of the architect's and builder's efforts.
A wood furnace should be the first thing you build if you embarked with nothing but coal, logs, and a single unit of coke. It will allow more fire safe construction materials to be built so that you can smelt the coal and forge picks.