How do I add new terminal IDs to a processing path?

First you need to GET the processing path ID for the merchant that you want to add terminal IDs to (GET /v2/merchants/{merchantIdentifier}). In the response you will find the parameter $.data.processingPaths[].identifier with the processing path ID.
With the processing path ID, you can then POST new terminal IDs to this processing path (POST /v2/processingPaths/{processingPathId}/terminalIds).