In order to move regions around, you will need to edit the page style that the regions appear on. Within these page styles, you will find HTML tags specific to the liveSite system. To change their positioning, you will need to find the specific tag that you want to move and then move it to the new position. These tags that you are moving may also have a few div tags wrapped around them. These div tags may apply styling the regions so you may need to move them as well.
Note: This may require knowledge of HTML.