C:\Program Files\Unity\Hub\Editor\2018.1.9f2\Editor\Data\Mono\lib\mono\2.0

Copy Npgsql.dll and System.Data.dll from this directory and put it into Assets/Plugins

Here is my test function:

    private const String SERVER = "localhost";
    private const String PORT = "5432";
    private const String USER = "postgres";
    private const String PASSWORD = "password";
    private const String DATABASE = "test";

    public NpgsqlConnection connection = null;

    // Use this for initialization
    void Start ()
    {
        connection = new NpgsqlConnection(
            "Server=" + SERVER + ";" +
            "Port=" + PORT + ";" +
            "User Id=" + USER + ";" +
            "Password=" + PASSWORD + ";" +
            "Database=" + DATABASE + ";"
        );

        connection.Open();

        NpgsqlCommand command = new NpgsqlCommand("SELECT name FROM test LIMIT 10", connection);

        // Prepare the command.
        command.Prepare();

        // Execute SQL command.
        NpgsqlDataReader dr = command.ExecuteReader();

        while (dr.Read())
        {
            String TestName = dr.GetString(0);
            Debug.Log("Test Name : " + TestName);
        }

        connection.Close();
    }