Haven't yet needed a signal slot mechanism between QML and Qt but here's how you can call C++ code from QML:

First you need your class:

Qt Code: 
  1. #include <QObject>
  2.  
  3. class MyClass : public QObject
  4. {
  5.     Q_OBJECT
  6. public:
  7.     explicit MyClass(QObject *parent = 0);
  8.  
  9.     Q_INVOKABLE void doThisAndThat(QString myString);
  10.     Q_INVOKABLE QString getThisAndThat();
  11.  
  12. signals:
  13.  
  14. public slots:
  15.  
  16. private:
  17.  
  18.     QString localThisAndThat;
  19. };
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And you can create the implementation as you wish, no need to use the Q_INVOKABLE on the implementation side, though.

The you need to introduce this class to QML like this:

Qt Code: 
  1. QDeclarativeView::rootContext()->setContextProperty("qmlReferenceName", myClass);
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So you just give a string of your choice to qmlReferenceName, and pass your class on myClass. After this, you have this class as a global scope variable within your QML code:

Qt Code: 
  1. Rectangle {
  2.    MouseArea {
  3.       anchors.fill: parent
  4.       onClicked: { qmlReferenceName.doThisAndThat("It works!") }
  5.    }
  6.  
  7.    Text {
  8.       text: qmlReferenceName.getThisAndThat()
  9.  
  10.    }
  11. }
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