Issues migrating site back to local server
As the OP noted in a comment, there is documentation available from Aquia that explains how to do this. For a better formatted answer please follow the above link.


  IMPORTING AN EXISTING SITE OR CODEBASE INTO ACQUIA DEV DESKTOP
  
  To run an existing site or new Drupal distribution on your local
  computer, complete the following steps:
  
  
  Ensure that your local computer contains a copy of your site's Drupal
  files and directories (codebase).
  
  
  Save your site's codebase in a place where you can find it and where
  you won't delete or move it unintentionally. This protects your site
  from accidental removal, and helps when you need to modify site
  content or change the installed modules.
  You cannot import zipped or compressed codebases into Dev Desktop.
  Ensure that your site's code is uncompressed.
  For more information about backing up the Drupal file system, see
  Drupal file system backup.
  
  
  Note: Dev Desktop does not move or copy your site's code into the Dev
  Desktop installation directory. Instead, Dev Desktop records where the
  Drupal directories are stored on your local computer.
  Open the Acquia Dev Desktop Control Panel, click Settings, and then
  select the Sites tab.
  Click Import. The Import site window opens.
  In the Codebase section, click Browse to select the source code
  directory (also known as [docroot]) of your Drupal installation. This
  directory contains Drupal's files and directories, including
  index.php, the /includes directory, and the /modules directory.
  After you select the your codebase, in the Subsite drop-down menu,
  select the site to import from the source code directory. For
  single-site codebases or Drupal distributions, select default. If
  you're importing a codebase that contains multiple subsites, select
  the subsite you want to import from the Subsites drop-down menu.
  
  Note: Dev Desktop can only import one site at a time.
  Configure the database settings for the site import process. The
  settings are based on the type of site or codebase you're importing
  into Dev Desktop.
  In the Database name field, enter a name for
  the database. If you're restoring a backed up database, the name does
  not have to match the backed up database's previous name.
  Under Domain, enter the elements (server, subdomain, and URL path) of
  the local URL you want to use for your site. For example, if you want
  to reach your site locally at http://my.example:8082/mysite, enter my
  for the Subdomain, example for the Server, and mysite for the URL
  path. The subdomain and URL path are optional.
  Click Import.
  
  Acquia Dev Desktop records the location of your site's Drupal
  codebase, creates its new database (if selected), and adds the site to
  the list of sites in the Sites tab.