How to add a class and title attribute to the link generated by next/previous post

previous_post and next_post are deprecated. you should be using previous_post_link and next_post_link. That function applies the {$adjacent}_post_link filter. You can use that to get what you want. A very, very crude example:

function construct_np_attr_wpse_92086($matches) {
  if ('prev' == $matches[1]) {
    $np = 'Previous';
  } else {
    $np = 'Next';
  }
  $ret="rel="".$matches[1].'" class="normalTip" ';
  if (!empty($np)) {
    $ret .= 'title="'.$np.' Project"';
  }
  return $ret;
}
function add_attr_to_np_links_wpse_92086($link) {
  return preg_replace_callback('/rel="([^"]+)"https://wordpress.stackexchange.com/",'construct_np_attr_wpse_92086',$link);
}
add_filter('next_post_link','add_attr_to_np_links_wpse_92086');
add_filter('previous_post_link','add_attr_to_np_links_wpse_92086');