Even if you originally started with a Fantastico install ... you can begin to maintain your own site and do your own upgrades ...
You can practice by making a test directory on your site /testing and a test database ... and copy all of the Full Zen Cart v1.3.0.2 to your /testing directory ...
Read through the /docs files to help you get started ...
When you install this test site ... install the demo products ...
These will help you learn a lot about Zen Cart, the features, product setup, etc.
When upgrading a Live site ... I always start with a /new_shop directory and copy my Live site to that directory ...
Then I make a new database and load a copy of my Live site database into it ...
Then I update the 2 configure.php files to match my /new_shop and my new database name, username and password ...
Now I practice upgrading ...
There are numerous detailed threads on upgrading sites in this manner that you might do some searches on ...