It would look like this:

$vps = mysql('SELECT * FROM people WHERE IsVP = 1');

foreach $vps as $vp:
  $salary_total = 0;
  foreach get_all_children($vp) as $child:
    $salary_total = $salary_total + $child['salary'];
  endforeach;
  print('Salary total: ' . $salary_total);
endforeach;

function get_children($employee) {
  return mysql('SELECT * FROM people WHERE reportsto = ?', ($employee));
}

function get_all_children($employee) {
  $children = get_children($employee);
  if $children:
    foreach $children as $child:
      $children = $children + get_all_children($child); // some sort of array concatenation operation.
    endforeach;
  endif;

  return $children;
}

I am confident that all of that can be done in a single, more elegant SQL query.

If the DBMS you're using supports recursion, you could write a stored procedure to do what you need. Some DBMSs will have hierarchical querying options. If you're running MS SQL, the online help will have an example of expanding a hierarchy. Presumably the same is true of Oracle and the like.