Go to Settings > Integrations and Keys, click New key, and search for New Relic. Click Continue, specify a key name, and click Save.
In the Integrations list, where your key is now included, click Authenticate..
Follow the instructions in the dialog to get your key.
Enter the key received as described above in the dialog in step 3 above and click Save.
Now that you've configured your integration, add one or more of the integration's actions to an automation, test the automation, and then add the automation to an incident type.