Exception Details: System.Data.SqlClient.SqlException: Login failed for user
One of our user from another domain (...)


To authenticate against a resource in another domain, either there must be a domain trust established (ask your Windows sysadmins), or pass-through authentication must be used (very likely not in this case). This is true for Windows in general, not just SQL Server.


  Do I need to setup my SQL Server 2008 Enterprise in order to allow domain user (...)


If there isn't an existing Windows user or group login for the user, then yes, you'll need to create a new login.


  Kindly note that there might be more than 50 domain users that may required to access the web application and therefore it would be inefficient to add each domain user to the database's user rights


I agree -- with this type of scenario, I would recommend setting up a group in AD, and then creating a Windows group login in SQL Server. This way, access is controlled by AD group membership, and you don't have to mess around with changing logins in SQL Server once it's set up.