I finally upgraded Yourls in an attempt to get back to the Twitter plugin. Simple to upgrade.

Backup yourls directory location.
Backup yourls MySQL database.
Remove everything from your yourls location.
Unzip the new yourls software.
Copy the config_sample.php to config.php. The configuration files are location in the includes directory.
Modify the config.php with your site specific settings.
I had to modify the following definitions:
YOURLS_DB_USE
YOURLS_DB_PASS
YOURLS_DB_NAME
YOURLS_SITE
$yourls_user_passwords

And, because I was upgrading from 1.2, I had to add the following definitions:
define(‘YOURLS_DB_TABLE_URL’, ‘url’);
define(‘YOURLS_DB_TABLE_NEXTDEC’, ‘next_id’);

Go to your yourls site:
http://yourls-url/admin
Login and upgrade.