¿Cómo preparar la declaración para la consulta de actualización?

Una UPDATE funciona igual que una inserción o selección. Simplemente reemplace todas las variables con ? .

$sql = "UPDATE Applicant SET phone_number=?, street_name=?, city=?, county=?, zip_code=?, day_date=?, month_date=?, year_date=? WHERE account_id=?";

$stmt = $db_usag->prepare($sql);

// This assumes the date and account_id parameters are integers `d` and the rest are strings `s`
// So that's 5 consecutive string params and then 4 integer params

$stmt->bind_param('sssssdddd', $phone_number, $street_name, $city, $county, $zip_code, $day_date, $month_date, $year_date, $account_id);
$stmt->execute();

if ($stmt->error) {
  echo "FAILURE!!! " . $stmt->error;
}
else echo "Updated {$stmt->affected_rows} rows";

$stmt->close();