Most of the trees in the area may be cut down with an axe. You can find it in your woodshed.
Approach the tree you want to cut down and start hitting it with an axe until it starts to fall down. Be careful, being crushed by a falling tree is lethal.
Keep cutting off the branches and stumps with an axe until a bare stem is left.
Divide the stem into logs by cutting it into highlighted spots.
You can transport such logs to the sawmill using a horse and process them there. You can also harvest logs on-site, but you will heave to carry the heavy fruits of your labour home. Using an axe on a log will give you firewood while using a handsaw will produce planks. The bigger the log the more resources may be harvested.