Ideally, Drupal would be installed under a generic alias name. But if this is not done, there are a hand full of places you need to alter for a full migration.
- Go as Administrator, administer -> settings -> filemanager and change the Public file system url box reference. You should do this before copying to a new server (as db access will not be possible afterward)
- Log on to your Drupal server as root, cd to the Drupal's root installation directory. Edit sites/default/settings.php and change $base_url
- Check a file named scripts/cron-curl.csh and change the reference
You should be ready to export Drupal as-is to another server.