uses
  ShellApi;
 
..
 
procedure TForm1.FormCreate(Sender: TObject);
begin
  DragAcceptFiles(Form1.Handle, true);
  Application.OnMessage := AppMessage;
end;

{ message handler procedure }
// Delphi 1: type DWord = longint; .. FileIndex := -1;

procedure TForm1.AppMessage(var Msg: Tmsg; var Handled: Boolean);
const
   BufferLength : DWORD = 511;
var
   DroppedFilename   : string;
   FileIndex         : DWORD;
   NumDroppedFiles   : DWORD;
   pDroppedFilename  : array [ ..511] of Char;
   DroppedFileLength : DWORD;
begin
   if Msg.message = WM_DROPFILES then
   begin
       FileIndex := $FFFFFFFF;
       NumDroppedFiles := DragQueryFile(Msg.WParam, FileIndex,
                                        pDroppedFilename, BufferLength);

       for FileIndex := 0 to (NumDroppedFiles - 1) do
       begin
           DroppedFileLength := DragQueryFile(Msg.WParam, FileIndex,
                                              pDroppedFilename,
                                              BufferLength);
           DroppedFilename := StrPas(pDroppedFilename);

           { process the file name you just received }
       end;
       DragFinish(Msg.WParam); { important to free memory }
       Handled := true;
   end;
end;