using NHibernate; 
  using NHibernate.Cfg;
  // ..........
  Configuration cfg = new Configuration().Configure();

var providerFactory = DbProviderFactories.GetFactory( "System.Data.SqlClient" );
using ( var connection = providerFactory.CreateConnection() )
{
  connection.ConnectionString = "тут строка соединения";
  //...
}

public string ConnectionString
{
  get
  {
    var configuration = new Configuration().Configure();
    var connectionString = configuration.GetProperty( "connection.connection_string" );
    if ( connectionString != null )
      return connectionString;
    var connectionStringName = configuration.GetProperty( "connection.connection_string_name" );
    return ConfigurationManager.ConnectionStrings[connectionStringName].ConnectionString;
  }
}

public string ProviderInvariantName
{
  get
  {
    switch ( GetNhibernateConfiguration().GetProperty( "connection.driver_class" ) )
    {
      case "NHibernate.Driver.SqlClientDriver":
        return "System.Data.SqlClient";
      default:
        throw new Exception( "Failed to determine provider invariant name" );
    }
  }
}