Here is a sample of main.cpp
that do exactly that (you will have to modify the new window though).
#include <QtGui>
int main(int argc, char* argv[]) {
QApplication app(argc, argv);
QWidget *firstWindow = new QWidget();
QLabel *text = new QLabel("Here is some text one the first window.");
QPushButton *button = new QPushButton("Button on the first window that display the other window");
QBoxLayout *layout = new QVBoxLayout();
layout->addWidget(text);
layout->addWidget(button);
firstWindow->setLayout(layout);
QWidget *secondWindow = new QWidget();
// add some things on the second window
// on button click, close the first window and show the second one
connect(button, SIGNAL(clicked(bool)), secondWindow, SLOT(show()));
connect(button, SIGNAL(clicked(bool)), firstWindow, SLOT(close()));
// display the first window at the start of the application.
firstWindow->show();
return app.exec();
}