How can I set an SQL Server connection string?

.NET DataProvider -- Standard Connection with username and password

using System.Data.SqlClient;

SqlConnection conn = new SqlConnection();
conn.ConnectionString =
  "Data Source=ServerName;" +
  "Initial Catalog=DataBaseName;" +
  "User id=UserName;" +
  "Password=Secret;";
conn.Open();

.NET DataProvider -- Trusted Connection

SqlConnection conn = new SqlConnection();
conn.ConnectionString =
  "Data Source=ServerName;" +
  "Initial Catalog=DataBaseName;" +
  "Integrated Security=SSPI;";
conn.Open();

Refer to the documentation.