[donatas]

хэлпы рулят

procedure TForm1.Button1Click(Sender: TObject);

begin
  FindDialog1.Position := Point(RichEdit1.Left + RichEdit1.Width, RichEdit1.Top);
  FindDialog1.Execute;
end;

procedure TForm1.FindDialog1Find(Sender: TObject);
var
  FoundAt: LongInt;
  StartPos, ToEnd: Integer;
begin
  with RichEdit1 do
  begin
    { begin the search after the current selection if there is one }
    { otherwise, begin at the start of the text }
    if SelLength <> 0 then

      StartPos := SelStart + SelLength;
    else

      StartPos := 0;

    { ToEnd is the length from StartPos to the end of the text in the rich edit control }

    ToEnd := Length(Text) - StartPos;

    FoundAt := FindText(FindDialog1.FindText, StartPos, ToEnd, [stMatchCase]);
    if FoundAt <> -1 then
    begin
      SetFocus;
      SelStart := FoundAt;
      SelLength := Length(FindDialog1.FindText);
    end;
  end;
end;