Steps and tips.
Before upgrading, check that your server meets all requirements for 3.11 in Site administration > Server > Environment.
See the release notes in the dev docs for both server and client software requirements.
Notes:
You can only upgrade to Moodle 3.11 from Moodle 3.6 or later. If upgrading from earlier versions, you must upgrade to 3.6 as a first step.
Before upgrading
We advise that you test the upgrade first on a COPY of your production site, to make sure it works as you expect.
Consider setting the upgrade key for your site.
Backup important data
There are three areas that should be backed up before any upgrade:
Moodle software (For example, everything in server/htdocs/moodle)
Moodle uploaded files (For example, server/moodledata)
Moodle database (For example, your Postgres or MySQL database dump)
See Site backup for more specific information.
Check for plugin updates
If you have Automatic updates deployment enabled, you will be able to update installed plugins automatically during the upgrade. Just make sure you check for available updates (via the button for it) at the Plugins check screen.
If you are updating plugins manually, it is a good moment now to check in the Moodle Plugins directory whether there is a 3.11 version available for any plugins (including themes) that you have previously installed on your site. If so, download the plugin package. In the next step, you will copy it to the appropriate location in your Moodle code (see Installing plugins).
The upgrade of the plugin will then happen as part of the Moodle upgrade process.
If an out-of-date plugin causes your upgrade to fail, you can usually delete the plugin code rather than uninstalling it from within Moodle so that the data associated with it is not deleted.
Install the new Moodle software
You can fetch the current version of the software at
wget http://sourceforge.net/projects/moodle/files/Moodle/stable311/moodle-latest-311.tgz
Standard install package
Move your old Moodle software program files to another location. Do NOT copy new files over the old files.(In my case i first made a local installation of my moodle site on a xmpp server and I created a new directory for the upgraded version of my moodle site)
Unzip or unpack the upgrade file so that all the new Moodle software program files are in the location the old files used to be in on the server. Moodle will adjust SQL and moodledata if it needs to in the upgrade.
Copy your old config.php file back to the new Moodle directory.
As mentioned above, if you had installed any plugins on your site you should add them to the new code tree (Moodle directory structure) now. It is important to check that you get the correct version for your new version of Moodle. Be particularly careful that you do not overwrite any code in the new version of Moodle and that you place the plugin folders in the correct directory (the same directory that they are in in the current installation.)(In my case in order to locate the extra plugins there was in my old site I firts found a list of the additional plugins from site administrator--> plugins--> additional plugiins.
Then I serched the plugins' names one by one to locate the directorie they were stored in the root folder of the local installation and copied the files at the apropriate directory of the new local installation).
Your moodledata folder should be located separately to your Moodle code folder and, as such, should not need anything done to it.
Moodle 3.0 will throw a warning if it is located in a web accessible folder and the moodledata should never be located in the
Moodle code folder. If you are moving your installation to a new server or new location on your server, then you will need to
follow the Migration documents.
Finishing the upgrade
The last step is to trigger the upgrade processes within Moodle. (In my case i vistited: localhost/mymoodlename/admin and the updating process started immediately)
If you put your site into Maintenance mode earlier; take it out now!
To do this just go to Site administration > Notifications.
Moodle will automatically detect the new version and perform all the SQL database or file system upgrades that are necessary. If there is anything it can't do itself (very rare) then you will see messages telling you what you need to do.
Assuming all goes well (no error messages) then you can start using your new version of Moodle and enjoy the new features!
Possible error
I was receiving in my browser this message error: this site is not redirecting properly.
Clearing browser's cache and cookies resolved the problem :)
source:https://docs.moodle.org/311/en/Upgrading, https://bobcares.com/blog/fix-redirect-loop-in-moodle-easily/