How is "remember me" functionality implemented in famous websites?

Set the userid in the cookie, and set the lifetime to be 10 years (or whatever) into the future. In your app you then check if that cookie exists, and if it does look up the user id and log them in automatically.

The other way to do it is to use the existing session support. If the 'remember me' box is checked, you change the session so that instead of it expiring at the end of the browser session, it expires way into the future.

ie. your login script probably looks like this:

  session_start();
  $username = filter_func($_POST['username']);
  $password = filter_func($_POST['password']);
  $user = $db->query('select userid from users where username = ? and password = ?', $username, $password);
  if($user) {
    //user is logged in
    $_SESSION['loggedin'] = true;
  } else {
    // show login page with error
  }

you need to change it to:

  $username = filter_func($_POST['username']);
  $password = filter_func($_POST['password']);
  $remember = (bool) $_POST['rememberme'];
  $user = $db->query('select userid from users where username = ? and password = ?', $username, $password);
  if($user) {
    //user is logged in
    if($remember) {
      $lifetime = 10 * 365 * 24 * 60 * 60;
      session_set_cookie_params(time() + $lifetime);
    }
    session_start();
    $_SESSION['loggedin'] = true;
  } else {
    // show login page with error
  }

the key function is session_set_cookie_params() which will let you alter the cookie that the session store uses prior to seeting it:

http://php.net/session_set_cookie_params

note: that you need to call it before you call session_start(). $lifetime just calculates the number of seconds in 10 years, and the time set is time() (ie. now) plus the number of seconds in 10 years.

note: filter_func is a function that you write that will filter input variables, and $db is whatever your db class or access method is.

note: you also need to filter $_SESSION. most devs have a class that they wrap $_SESSION in rather than using it directly.