//from dialog.h
class Dialog : public QDialog
{
    Q_OBJECT

public:
    explicit Dialog(QWidget *parent = 0);
    ~Dialog();

public slots:
  void on_pushButtonDialog_clicked();
  void test();
signals:
   void trigger();
private:
    Ui::Dialog *ui;
};
//from dialog.cpp
Dialog::Dialog(QWidget *parent) :
    QDialog(parent),
    ui(new Ui::Dialog)
{
    ui->setupUi(this);
    connect(ui->pushButtonDialog, SIGNAL(clicked()), this, SIGNAL(trigger()));
}

Dialog::~Dialog()
{
    delete ui;
}

void Dialog::test()
{
  ui->lineEdit->setText("this is a test");
}

void Dialog::on_pushButtonDialog_clicked()
{
  ui->lineEdit->setText("button click");
}

//from mainwindow.h

class MainWindow : public QMainWindow
{
    Q_OBJECT

public:
    explicit MainWindow(QWidget *parent = 0);
    ~MainWindow();

private:
    Ui::MainWindow *ui;

private slots:
  void on_pushButtonMainWindow_clicked();
signals:
  void trigger();

};

//from mainwindow.cpp
void MainWindow::on_pushButtonMainWindow_clicked()
{
  Dialog dialog(this);
  connect(this, SIGNAL(trigger()), &dialog, SLOT(test()));
  dialog.exec();
}