You will have to run a STSADM script to move users from the OLD-AD to the NEW-AD, like this:
STSADM –o migrateuser –oldlogin OLDDOMAIN\user1 –newlogin
NEWDOMAIN\user1 –ignoresidhistory
This will do just fine on SharePoint Foundation. But if you have a User Profile Service Application, you may run into trouble. My experience tells me it doesn't work that well, and you need to clean up the user profiles that doesn't get imported correctly several times by running the following PowerShell script:
# Clean up accounts that is not imported correctly
$upsa = Get-SPServiceApplication | Where-Object {$_.TypeName -like
"User Profile Service Application"}
# List all user accounts that is not imported correctly
Set-SPProfileServiceApplication $upsa -GetNonImportedObjects $true
# Remove user accounts not imported correctly
# Uncomment line below to run
Set-SPProfileServiceApplication $upsa -PurgeNonImportedObjects $true
# Run a full User Profile Service Syncronisation, and make sure users
# end up in Profile database.
# If not, users who log in will create new NonImportedObject accounts
This won't remove users activity on content (as author and editor), nor will it delete content added by the user. It simply frees the old profile from the User Profiles DB making it possible for the new profile to take ownership.
More to read (from my own blog): SharePoint 2010: Migrate Users to new Active Directory Environment