The user field holds an array of user IDs.
If you want to add a user ID to the field that already has values.
// get the user field without formatting
$users = get_field('user_field', $post_id, false);
// test to see if empty
if (empty($users)) {
$users = array();
}
// add a user
$users[] = $new_user_id;
// use field key to update field
// it will not update using field name
// if it did not already have a value
update_field('field_XXXXXXX', $users, $post_id);