As the fan page owner or admin, you can simply reply to any messages in your inbox by going to the message, and clicking the reply icon. You can either reply directly on your fan page, or in the "inbox" section of the dashboard.
After clicking reply, the reply box will slide open. Here, you can choose whether to reply with a text or audio message.
Message replies aren't meant to be a discussion or comment thread. They are purely meant for you to appreciate your fans with a direct reply.
After you reply, your fan will receive an email notification of your reply.
To delete your reply, simply click on the context menu and click "delete".