This guide was originally written for a Djeen 1.X to 1.Y version update.
If you want to follow a simple update guide (1.X.x to 1.X.y), please follow this guide.
Important: this part of the process shall not be neither skipped nor underestimated at all.
This step is just a safety measure, since database restoration is fully managed by the update system (see below for more details). But it's a database, so caution is never a bad thing.
For the sake of an example, say our Djeen database has the following associated characteristics:
There is an example name for our backup file: djeen_dump.sql. And an example path to create this backup into: tmp/.
Let also define an example port:
Under the prompt, type the following command:
$ mysqldump -h localhost -P 3306 -u test -p qwerty -r tmp/djeen_dump.sql djeen_db
Notice the difference between the uppercase P (for the port option) and the lowercase p (for the password option).
Example port:
Under the prompt, type the following command:
$ pg_dump -h localhost -p 5432 -U test -f tmp/djeen_dump.sql djeen_db
Notice the uppercase U (for the user option).
Connect into your Joomla! website administration part with an admin account.
Then, go into the 'System information' section of Djeen component. You should see a 'Tools' title frame on the right, with a 'Component backup' line.
Click on the 'Create and download' button; this should trigger the download of the backup:
Save it.
Stay into Joomla! administration, and go into the 'Extension manager' section. Upload the Djeen archive of the new version you want to install.
If all goes as planned, you should see the following message:

Otherwise, you should see an error message.
Normally, when an update fails, the system automatically restores your database in its pre-update state.
If not, it should be indicated in the error message, and it's a more serious problem; in this last case, there is nothing to do except waiting for the development team to intervene.
If the database was successfully restored, just go into the 'Extension manager' section again, and upload the Djeen archive of the component backup you created earlier. If you forgot to perform such a backup (big mistake) but you have an internet connection, you still can go at http://djeen.sourceforge.net to get the proper archive (don't forget to choose the archive corresponding to the pre-update version).
Once the archive uploaded, Djeen should be fully restored in its pre-update version, and should at least be usable this way.