docs.joomla.org/Upgrade_Instructions
Always back up your site before updating.
www.akeebabackup.com/akeeba-backup-for-joomla/index.html
Usually what I do is back up the site, upload the upgrade to a folder in the root (I have a folder named 'upgrades')
Then through my host's CP, I just extract the contents of the latest upgrade (from the 'upgrade' folder) to the root, overwriting the existing files.
It's much faster than downloading the upgrade, extracting it, and then using an FTP client to upload all the files.