Upgrade is to bring an ownCloud instance to a new major release, e.g. ownCloud 5.0.14a → 6.0.2. Always do backups anyway.
To upgrade ownCloud, follow those steps:
Make sure that you ran the latest point release of the major ownCloud version, e.g. 5.0.14a in the 5.0 series. If not, update to that version first (see above).
Make a backup of the ownCloud folder and the database.
Download the latest version to the working directory:
Deactivate all third party applications.
Delete everything from your ownCloud installation directory, except data and config.
Unpack the release tarball in the ownCloud directory (or copy the files thereto). Assuming that your installation directory is called ‘owncloud’ and that it’s inside your working directory, you could execute this command:
tar xfj owncloud-latest.tar.bz2
Set the permissions properly
With the next page request the update procedures will run.
If you had 3rd party applications, check if they provide versions compatible with the new release. If so, install and enable them, update procedures will run if needed.
Note: Since I used Turkey owncloud from my VPS provider, I deleted everything inside owncloud folder except data folder. The upgrade is no brainer.