We have a function that asks the user if he wants to save. If he says yes we save, then we return to the calling function whether it is ok to clear.

Menu New was clicked:

Private Sub mnuNew_Click(sender As Object, e As EventArgs) Handles mnuNew.Click
  'Start a new list if not changed or user doesn't want to save
  Dim canClear As Boolean = True
  If changed Then canClear = AskToSave()
  If canClear = True Then
    ListBox1.Items.Clear()
    currentFile = ""
    changed = False
  End If
End Sub

Menu Open was clicked (changed!):

Private Sub mnuOpen_Click(sender As Object, e As EventArgs) Handles mnuOpen.Click
  'Opens selected file and adds to list box if not changed or user doesn't want to save
  Dim oktoClear As Boolean = True 'this will be the value if there has been no change
  If changed Then
    oktoClear = AskToSave()
  End If
  If oktoClear Then
    ListBox1.Items.Clear()
    If OpenFileDialog1.ShowDialog() = DialogResult.OK Then
      currentFile = OpenFileDialog1.FileName
      Dim S As String = ""
      Me.Text = currentFile
      FileOpen(1, currentFile, OpenMode.Input) 'open the file for input
      While Not EOF(1) 'EOF=End of file, this loops to read all recordds
        S = LineInput(1) 'read from file 1
        Me.ListBox1.Items.Add(S) 'add the item read to the combo box
      End While
      FileClose(1) 'close file 1
      If Me.ListBox1.Items.Count > 0 Then 'make sure the file was read
        Me.ListBox1.SelectedIndex = 0
      End If
      changed = False
    End If
  End If
End Sub

See the complete code at this point.

NEXT: Build the Menu