How to connect to a SQL Server Database When the Server is not on the Domain

This article explains how to connect to a Microsoft SQL Server database when
the server is not on the domain. These instructions are particularly useful when
troubleshooting the "Connect to Server" error, which can be Error Number:
11001 (or 53), Severity: 20, State: 0

"A network-related or instance-specific error occurred while establishing
a connection to SQL Server. The server was not found or was not
accessible. Verify that the instance name is correct and that SQL Server
is configured to allow remote connections. "

 "(provider: Named Pipes Provider, error: 40 - Could not open a
connection to SQL Server) (Microsoft SQL Server, Error: 53)" or
"(provider: TCP Provider, error: 0 - No such host is known.) (Microsoft
SQL Server, Error: 11001)"