When an individual submits a Contact Us Form on your website the person your administrator has nominated to be notified of new enquiry will receive a chatter notification.
Simply click on the notification bell to go to the chatter post.
From the chatter post you will be able to go directly to the new enquiry record by clicking on the person's name at the top left of the chatter post eg. Sally Bensen.
Now you can action their enquiry.