Check the following and fix the issue accordingly.
1) Make sure your server name is correct, e.g., no typo on the name.
2) Make sure your instance name is correct and there is actually such an instance on your target machine. [Update: Some application converts \\ to \. If you are not sure about your application, please try both Server\Instance and Server\\Instance in your connection string]
3) Make sure the server machine is reachable, e.g, DNS can be resolve correctly, you are able to ping the server (not always true).
4) Make sure SQL Browser service is running on the server.
5) If firewall is enabled on the server, you need to put sqlbrowser.exe and/or UDP port 1434 into exception.
6) Also check whether TCP/IP is enabled and the port is added to the firewall exception (if it is not using the default 1433 port)
You can download PortQry from http://support.microsoft.com/kb/832919, run "portqry.exe -n yourservername -p UDP -e 1434". If this command returns information and it contains your target instance, then you can rule out possiblity 4) and 5) above, meaning you do have a SQL Browser running and your firewall does not block SQL Browser UDP packet. In this case, you can check other issue, e.g. wrong connection string.