Executing the FocusHelp method causes the currently active control on the form to pop up it's Popup Help (assuming a control actually has the focus and some Popup Help text has been specified for it).
Example
The following code is all that is required to initiate Popup Help for the active control. It assumes the TMFMHelp control is named MFMHelp1 and that it is in response to a press of the F1 key. (Note you need to set KeyPreview to True for the form):
procedure TForm1.FormKeyDown(Sender: TObject; var Key: Word;
Shift: TShiftState);
begin
if Key = VK_F1 then MFMHelp1.FocusHelp;
end;