It is possible to fell trees and, in doing so, derive valuable timber - for various uses including construction, item making, craftsmanship and fires. Felling trees requires a modicum of skill and the ability is part of the Farming skillset. You will need an axe to carry out the task.
A word of warning, however: the trees of Avalon, particularly those in the more ancient woodlands, are not all slumbering and passive receivers of the axe. Some are awake; some are roused to great violence by axe-blows; others consider themselves shepherds or protectors of the forest and will strike down unwary woodcutters. It is up to you to find safe areas within the forest, to ensure your axe does not strike where it will cause you more damage than harm. Ask a friendly Animist, Ranger or Druid since those forest experts will be point out safer areas to ply the woodsman's trade.
It may be, of course, that you know full well a tree has been awakened, roused and possessing of intelligence of its own. You may consider this awakened tree or ent (see HELP ENTS) as an adversary. Trees of all kind are vulnerable to fire and the axe, to varying degrees, and the feeling of an ent or an awakened tree has repercussions far beyond the mere provision of lumber.