On your dialogue form, expose the MonthCalendar selection via a read-only property:
Code:
Public Class CalendarDialogue

    Public ReadOnly Property SelectedDate As Date
        Get
            Return MonthCalendar1.SelectionStart
        End Get
    End Property

End Class
Your main form will then do something like this:
Code:
Private Sub changeDateButton_Click(sender As Object, e As EventArgs) Handles changeDateButton.Click
    Using dialogue As New CalendarDialogue
        If dialogue.ShowDialog() = DialogResult.OK Then
            Label1.Text = dialogue.SelectedDate.ToShortDateString()
        End If
    End Using
End Sub
To make ShowDialog return OK, set the DialogResult property of the OK Button on the dialogue form to OK or else set the form's DialogResult property to OK in the OK Button's Click event handler. The first option is preferable if you wouldn't be doing anything else in the Click event handler.