The idea in that snippet is a sound one, except for the fact the search terms are hardcoded into the sql string and there are only 3 of them

You have to build the statement on the fly, like this
PHP Code:
<?php
// simple search
// $query = search query from form
$query 'hello world';

$sql 'SELECT * FROM table WHERE ';

// split into terms on space
$terms explode(' '$query);

// loop through array building sql statement
for ($i=0$i count($terms); $i++) {
    
$sql $sql."Field LIKE '%$terms[$i]%' AND ";
}
//remove final 'AND '
$sql substr($sql0, -4);
// add ending SQL
$sql $sql.'ORDER BY Field';

// do whatever with SQL string
print $sql;

?>