delete is just another SQL statement, so all you really need is the form to send you whatever info you need to identify the row to be deleted -- usually whatever the primary key is. So when you populate the select box, you might set the value of each option to that primary key, then display the user-friendly name. Then you'd use that submitted value in your delete query, something like:
$sql = "DELETE FROM table_name WHERE id = " . (int) $_POST['user_id']; // making sure it's an integer
if(mysqli_query($sql) == false) {
// some sort of error-handling here?
}
That's just the basics: you could use a prepared statement with a bound parameter, etc....