Why can't I connect to SQL Server 2008? I initially installed SQL Server 2008 R2 with Windows authentication mode and have successfully changed it to mixed mode (per http://msdn.microsoft.com/en-us/library/ms188670.aspx).

After this I am able to log in to my SQL Server with SQL Server authentication. But from another computer which is on my network, I am not able to connect my server.
For security reasons SQL Server 2008 no longer opens TCP port 1433 upon installation.  You will need to create a firewall rule that allows communication over TCP port 1433 (and UDP port 1434 if you wish to use the browser service) to allow applications to communicate with SQL Server.