The WPS endpoint is available is available here. You can acccess the service through the web application or through the end-user api. You will need to sign into the web application to retrieve an api key. If you're accessing protected data you will need to authorization the compute service to request a certificate on your behalf, this is covered in the getting started document.
The compute service is expecting CF compliant data that is available through an OpenDAP URL.
On the top left of the page you will find a help button that will present a little walk through. If you're still experiecing issues or have a question please open an issue on GitHub
This input is not expecting a URL (feature that is being worked on), rather it is expecting the "id" of a DataSet found through ESGF search results.
If your input data is CMIP5, CMIP3 or any data that requires authorization, this may be caused by a known issue and retrying the same operation may result in success. If the following is true you may track the status of the issue here otherwise report a new bug.
Please open an issue using GitHub
Please report this bug using GitHub
Please create a feature request using GitHub