The examples are a good place to start. The minimal you'll need to have is:

require './facebook.php';

$facebook = new Facebook(array(
  'appId'  => 'YOUR_APP_ID',
  'secret' => 'YOUR_APP_SECRET',
));

// Get User ID
$user = $facebook->getUser();

To make API calls:

if ($user) {
  try {
    // Proceed knowing you have a logged in user who's authenticated.
    $user_profile = $facebook->api('/me');
  } catch (FacebookApiException $e) {
    error_log($e);
    $user = null;
  }
}

Login or logout url will be needed depending on current user state.

if ($user) {
  $logoutUrl = $facebook->getLogoutUrl();
} else {
  $loginUrl = $facebook->getLoginUrl();
}