How do I connect to SQL Server through a firewall?

A. Basically you have to open up the ports that SQL Server uses. If you've done this and it still doesn't work then look at the firewall logs to see what packets it is dropping or do a network trace either side of the firewall to see what packets are not getting through. (You may want to disable/allow all through the firewall during testing to see what extra packets are allowed through).

Which ports to open depends on the net-lib you are using :-

For tcp-ip sockets the default port for SQL Server is 1433.

For multi-protocol (rpc) the ports are normally variable, but you can fix them. See Q164667 in the Microsoft knowledgebase for details.

For named-pipes over ip 137/138/139 are used. As these are the same ones used for file/print it is not recommended you allow these through the firewall.