The easiest way I've found to upgrade is backup your copy your htdocs folder and keep as a backup in case you have to revert.
Export your SQL database as a backup as well, just in case.
Copy the contents of the 13.1 download into your existing htdocs folder and overwrite everything.
When you open your index page it will go straight to the install.php file.
If it goes wrong just rename the htdocs folder you copied and it'll be back to normal.