You need to look at the findby methods that CakePHP provides.
in addition to your standard findAll() you have a number of "magic" findby methods which allow you to specify a column in the table to search by:
$this->User->findBySurname($surname);
You also have findBySql(statement) which allows to you use a custom SQL statement. You could use this to execute a LIKE statement as follows:
$users = $this->User->findBySql("SELECT * FROM USERS u WHERE u.SURNAME LIKE '%" . $surname . "%' ORDERBY SURNAME");
That will return you a list of matching users which you can then display to the user. It's not the most efficient query, but it works.