A common cause of this error is the use of symlinks without enabling this in the admin area…
System > configuration > developer > Template Settings
The error gets triggered in
app\code\core\Mage\Core\Block\Template.php around line 243 ( see here ) - so if its not an issue with symlinks then this would be a good place to start debugging.
If you are not using xDebug then where the exception gets caught around line 250 you should either log or var_dump the values of:
Then make sure they both exist (paying attention to the case)
Failing that you might want to look at permissions.
I suspect you have a third party module installed acting as a aitcommonfiles and as the error suggests the template file
design--frontend--base--default--template--checkout--onepage--shipping_method.phtml does not exist in the location
This is a third party module I would re-install it, or find the missing template file and put it in the correct location, or contact the module provider for assistance.