To find your Airtable API key, navigate to your Airtable account page. Look in the "API section", if you already have an API key defined click in the purple text box and the API key will appear. If you do not see the purple text box click on the "Generate API Key" button and your API key will be generated for the first time.
Once you've generated a key, you have the option of regenerating your key or deleting your key at any time. To regenerate your key, click the "Regenerate API key" option.