SQL Server 2012 Enterprise: Copy Databases to New SQL Server, Same Domain, Users, Etc
Run this on your current instance:

select
    'CREATE LOGIN ['+p.name+'] FROM WINDOWS;'
from sys.server_principals as p
where type in ('U','G')


Take it's output and run it on the new instance.  Those AD accounts will now have logins on both instances. (This is a good opportunity to audit your access and ensure all those users really are needed.)

Backup your databases (a proper SQL Server backup, not a copy of mdf and ldf files) and restore these to the new instance. You may have to get creative with the restores if the drive names have changed.  If there are a lot of DBs some RESTORE FILELISTONLY and a script will save much time.

Finally, on each DB, script an ALTER USER to reconcile LOGINS to USERS.  This can be meta-scripted as above.

Test connections to the new instance.  Update the applications' connection strings.  Take the old DBs offline and, after a few days, tidy away the old server.