Sendy is email software similar to Mailchimp, Mailerlite and Active Campaign (all of which are supported by SpeakOut!).
You need 3 pieces of information to connect your petition to Sendy; the installation URL, your API Key and the list IDGroup ID.
You get that information in your Sendy.com dashboard.
You add the information in the dashboard > SpeakOut! > Petition > edit > 3rd Party Extras tab.