SQL Server 2008 ODBC
You can ask the Database Administrator for the environment what your SQL Server Login details are for using SQL Server Authentication.

Alternatively, you could connect to the SQL Server Instance via RDP and Windows Authentication and then create a new SQL Server Login for you to use remotely.

To confirm, you cannot use Windows authentication remotely (from outside of the domain the instance resides in) unless you are connecting from a domain with a trust relationship defined.