How do I handle the event of the user pressing the ‘X’ (close) button?

If you have a QMainWindow you can override closeEvent method.

#include <QCloseEvent>
void MainWindow::closeEvent (QCloseEvent *event)
{
    QMessageBox::StandardButton resBtn = QMessageBox::question( this, APP_NAME,
                                                                tr("Are you sure?\n"),
                                                                QMessageBox::Cancel | QMessageBox::No | QMessageBox::Yes,
                                                                QMessageBox::Yes);
    if (resBtn != QMessageBox::Yes) {
        event->ignore();
    } else {
        event->accept();
    }
}

If you’re subclassing a QDialog, the closeEvent will not be called and so you have to override reject():

void MyDialog::reject()
{
    QMessageBox::StandardButton resBtn = QMessageBox::Yes;
    if (changes) {
        resBtn = QMessageBox::question( this, APP_NAME,
                                        tr("Are you sure?\n"),
                                        QMessageBox::Cancel | QMessageBox::No | QMessageBox::Yes,
                                        QMessageBox::Yes);
    }
    if (resBtn == QMessageBox::Yes) {
        QDialog::reject();
    }
}