I'm new to PHP, so forgive me for any missteps.
I'm using a Wordpress plugin called Short Code Exec
I am writing a pretty simple piece of code that is dependent on a specific PHP library (call it XYZ)
I notice that I need to use Composer to install this library
the library's docs say run
php composer.phar require blahblah/XYZ
But, how do I do this within this plugin?
You don't run composer within the plugin, you will need to either run it locally and upload the files it downloads/creates or run it on your server.
You will then include the autoload file like you would with a normal php project with in the plugin (ie. require '/vendor/autoload.php';) and then you run the rest of your code and the classes will be autoloaded for you.