How should one act who found valuable furniture near his residence and took it, then learned of its value but is ignorant of its owner, so as to clear his conscience?

If you know or strongly believe that the furniture has been discarded by its owners, who left it for anyone to take, then there is no blame upon you for taking it and benefiting from it. However, if you know that its owner has not permitted its use and it was lost from them, then it falls under the ruling of a Luqatah (lost and found item). It must be announced for a full lunar year in the place where it was found and in places where people gather. If the period expires, it is permissible to dispose of it, while guaranteeing it to its owner if they can be reached. The announcement of the Luqatah must be initiated promptly for a full year from the date it was found. If the announcement is delayed, then the compensation will be from the second year. If its owner is not found after that, then the more cautious approach is to give it as charity on behalf of its owner.