PHP 5+ is now a requirement so please check you have PHP 5+ installed otherwise you won't be able to install or upgrade to the latest version.
If you already have 3.0, 3.1, 3.2 or 3.3 installed you can upgrade to 3.4. To do so download the 3.4 version of the script and upload everything except db.php, you can keep your own version of that file (you also don't need to reupload the install directory). Once everything has been uploaded run update/index.php from your browser, here it will ask you to enter the version number of the script you currently have installed it will then update the database with all the necessary changes. If all has gone well you should be prompted with a message telling you the upgrade is complete and to also delete the update file.
Remember to backup both your files and database before running the update.