[lmikle]

Так?

Код:

type
  TForm1 = class(TForm)
    ...
    procedure Button1Click(Sender : TObject);
    procedure FormCreate(Sender : TObject);
  private
    FNumber : Integer;
  end;
...
procedure TForm1.FormCreate(Sender : TObject);
begin
  FNumber := 0;
end;

procedure TForm1.Button1Click(Sender : TObject);
begin
  Inc(FNumber);
  Edit1.Text := IntToStr(FNumber);
end;