The quickest and easiest way is to copy the data and log files to the new server and attach them:
http://msdn.microsoft.com/en-us/library/ms187858.aspx
Or you can back up the database and then restore it to the new instance, this does not require you to detach and take off line the database you are copying.
Once the database is moved then the database users in the new instance will most likely not match to the instance logins from the old instance. Since this is a different domain you will probably not want the previous domain logins as they might not
be available, unless there is a trust between domains. You can transfer logins, both SQL and domain, using the SSIS Transfer Logins control flow task:
http://technet.microsoft.com/en-us/library/ms137870.aspx
Hope this helps.
David Dye http://sqlsafety.blogspot.com/