The Server name and Instance shows up in MSSMS when you connect to your database it looks like this.
So as you can see my Connection String would look like this:
Data Source=MANCOW2\SQLEXPRESS; Database=DairyCreme
I did not include Password or User Id because I am using windows authentication. However if your using mixed mode you can include those.
You need to ensure a few things are working first.
1. in MSSMS right click your server and choose properties then go to Connections and ensure Allow remote connections to this server is enabled.
2. Ensure the following services are active and running.
SQL Server Browser
SQL Server Agent
3. Go to run and type mmc and press enter to open the Microsoft management console. Go to File > Add new snapin and choose SQL Server Configuration manager
4. Expand the Native CLient 11.0 and click on Client Protocols and ensure TCP/IP is enabled.