string connectionstring ="data source=Servername;initial catalog=Northwind; integrated security=SSPI;persist security info=False; Trusted_Connection=Yes."

Where datasource will be computer name or IP Address, and initial catalog is the name of database.

If you’re using SQL Server 2005 Express Edition, your connection string will include an instance name, as shown here: SqlConnection myConnection = new SqlConnection();
myConnection.ConnectionString = @"Data Source=localhost\SQLEXPRESS;" + "Initial Catalog=Pubs;Integrated Security=SSPI";

Storing the Connection String Typically, all the database code in your application will use the same connection string. For that reason, it usually makes the most sense to store a connection string in a class member variable or, even better, a configuration file. You can also create a Connection object and supply the connection string in one step by using a dedicated constructor:
SqlConnection myConnection = new SqlConnection(connectionString); // myConnection.ConnectionString is now set to connectionString. You don’t need to hard-code a connection string. The < connectioString >section of the web.config file is a handy place to store your connection strings. Here’s an example
< configuration >
< connectionStrings >
< add name="Pubs" connectionString="Data Source=localhost;Initial Catalog=Pubs;Integrated Security=SSPI" / >
< / connectionStrings>
...

 < /configuration >

You can then retrieve your connection string by name. First, import the System.Web.Configuration namespace. Then, you can use code like this:
string connectionString = WebConfigurationManager.ConnectionStrings["Pubs"].ConnectionString;