Before you do any changes to the code at all, ensure you've taken a backup copy of both the site & database.
Open the downloaded zip file on your computer and extract the files into a new folder on your desktop. If you can't open zip files you may need to download a zip client such as WinZip.
Within your hosting control panel, load phpMyAdmin and select your new database. In the right-hand section click on 'import'. Attach the the relevant sql patches from the directory `/offline/version_sql_statements/` and submit the form. Choose the patches between your current script version number and the latest, ensuring you do them in version number order.
Using an FTP client such as FileZilla, upload all the files to your webroot (normally public_html folder) apart from the 'offline' & 'install' folder and the '_config.inc.php' file.
Using your FTP client, set permissions to CHMOD 777 on the following folders: '/files' & '/plugins'.