Other implementations have you editing your rsyslog.conf file, but that's not always an option of you can't SSH into the server, plus, it turns on the firehose of things that aren't necessarily related to your app.
First, add the Travoltron\Laratrail\LaratrailServiceProvider::class, to config/app.php and you're all set.
Second, call php artisan vendor:migrate to publish the config file.
End of the gif, I highlighted a url that was in the format of logsX.papertrailapp.com:XXXXX
Finally, you'll need these to add to your .env file:
PAPERTRAIL_DOMAIN to logsX.papertrailapp.com, replacing X with what returns when you add a log destination. Leave off the port and colon.
PAPERTRAIL_PORT to the port of your log destination (that's the part after, but not including :).