A user can simply send a message using the Message button on a page. Important fact is that in order to send a message it is not required to have geliked page. As the owner of a page you get a notification when a message has arrived and can be reacted.
Comments
All in all a good way to communicate with customers if there is a minor restriction. It is as it seems not possible as owner of a page to contact a user, but can therefore only be sent in response messages. It therefore seems that there is again a private message can be sent to a user who has posted a response on the page.
Alternative
Currently there is no option for a user to contact the owner of a page. This could potentially be just like the owner of a page for administrators has chosen to highlight on the left. In that case, you as a user click through to a manager's personal profile and thus a private message here, if the administrator allows it to his personal profile.
It is not known if this functionality is widely deployed.