To create your EmailOctopus API key, login to your EmailOctopus Account then click on API from the left sidebar. Click on Create a Key and copy the API key.
Go to Ninja Forms > Settings > EmailOctopus and enter your API key.
Go to Emails & Actions and click on the plus button in the bottom right and add the EmailOctopus Action
Select the appropriate list from EmailOctopus then add the Merge Tags to map the Ninja Forms fields to the appropriate EmailOctopus fields.
For information on how to setup your lists in EmailOctopus, please reference their support documentation.