Maximize the form and hide the title bar.  The maximize line is done from memory, but I'm pretty sure WindowState is the property you want.
There's also this article, but that seems too complicated to me.
procedure TForm1.FormCreate(Sender: TObject) ;
begin
   //maximize the window
   WindowState := wsMaximized;
   //hide the title bar
   SetWindowLong(Handle,GWL_STYLE,GetWindowLong(Handle,GWL_STYLE) and not WS_CAPTION);
   ClientHeight := Height;
end;
Edit:  Here's a complete example, with "full screen" and "restore" options.  I've broken out the different parts into little procedures for maximum clarity, so this could be greatly compressed into just a few lines.
unit Unit1;
interface
uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls;
type
  TForm1 = class(TForm)
    btnGoFullScreen: TButton;
    btnNotFullScreen: TButton;
    btnShowTitleBar: TButton;
    btnHideTitleBar: TButton;
    btnQuit: TButton;
    procedure btnGoFullScreenClick(Sender: TObject);
    procedure btnShowTitleBarClick(Sender: TObject);
    procedure btnHideTitleBarClick(Sender: TObject);
    procedure btnNotFullScreenClick(Sender: TObject);
    procedure btnQuitClick(Sender: TObject);
  private
    SavedLeft : integer;
    SavedTop : integer;
    SavedWidth : integer;
    SavedHeight : integer;
    SavedWindowState : TWindowState;
    procedure FullScreen;
    procedure NotFullScreen;
    procedure SavePosition;
    procedure HideTitleBar;
    procedure ShowTitleBar;
    procedure RestorePosition;
    procedure MaximizeWindow;
  public
    { Public declarations }
  end;
var
  Form1: TForm1;
implementation
{$R *.dfm}
procedure TForm1.btnQuitClick(Sender: TObject);
begin
  Application.Terminate;
end;
procedure TForm1.btnGoFullScreenClick(Sender: TObject);
begin
  FullScreen;
end;
procedure TForm1.btnNotFullScreenClick(Sender: TObject);
begin
  NotFullScreen;
end;
procedure TForm1.btnShowTitleBarClick(Sender: TObject);
begin
  ShowTitleBar;
end;
procedure TForm1.btnHideTitleBarClick(Sender: TObject);
begin
  HideTitleBar;
end;
procedure TForm1.FullScreen;
begin
  SavePosition;
  HideTitleBar;
  MaximizeWindow;
end;
procedure TForm1.HideTitleBar;
begin
  SetWindowLong(Handle,GWL_STYLE,GetWindowLong(Handle,GWL_STYLE) and not WS_CAPTION);
  ClientHeight := Height;
end;
procedure TForm1.MaximizeWindow;
begin
  WindowState := wsMaximized;
end;
procedure TForm1.NotFullScreen;
begin
  RestorePosition;
  ShowTitleBar;
end;
procedure TForm1.RestorePosition;
begin
  //this proc uses what we saved in "SavePosition"
  WindowState := SavedWindowState;
  Top := SavedTop;
  Left := SavedLeft;
  Width := SavedWidth;
  Height := SavedHeight;
end;
procedure TForm1.SavePosition;
begin
  SavedLeft := Left;
  SavedHeight := Height;
  SavedTop := Top;
  SavedWidth := Width;
  SavedWindowState := WindowState;
end;
procedure TForm1.ShowTitleBar;
begin
  SetWindowLong(Handle,gwl_Style,GetWindowLong(Handle,gwl_Style) or ws_Caption or ws_border);
  Height := Height + GetSystemMetrics(SM_CYCAPTION);
  Refresh;
end;
end.