The first thing to do is to create your combo box.  If you try to do the simple
zero argument constructor, you're going to get a box with zero choices, a blank
dropdown.  This is what happens when you use the QStandardItemModel, which
is empty by default.  You can choose either to use the QStandardItemModel
or create your own subclass of QAbstractItemModel.
QComboBox* comboBox = new QComboBox;
Remember that a combo box represents a choice between several items of a list.
So you need some way to specify that list.  You have a choice of abstraction
levels here.  The simplest way is to use the QStandardItemModel directly, via
the convenience methods provided by QComboBox.  In order of complexity your
other options are.
- Use QStringListModel directly
 - Subclass QStringListModel
 - Subclass QAbstractListModel
 - Subclass QAbstractItemModel
 
Using QStringModel directly is simple.
QStringList list = {"foo", "bar", "baz"};
QAbstractItemModel* myModel = new QStringListModel(list, comboBox);
comboBox->setModel(myModel);
What if we want to set the selected item?
comboBox->setCurrentIndex(1);
This will set the box to select bar, given the model above.  That is, indices
are zero-based.