If you update from 1.2.0  to 1.2.1 you only need to edit the PHP side.

1. Get the PHP.zip from the latest version and unzip it.
2. Use Filezilla or any other FTP program and connect to your site.
3. Download your config.php file from the site to your local computer (So we can move most of the values to the new config file)
4. Open the new config.php file and the old config.php and start move values from the old to the new.
5. In Filezilla: Upload the new PHP folder and replace any old files.
6. Done.

If you update from an earlier version you need to replace the old GML with the new one. And depending on how you added it this can be a little tricky. But if you kept the WebAPI folders intact in the project you should be able to just remove them and import the new ones. I think most of the old features use the same arguments so they should work as before.