This series of articles ultimately got me on the right track:

**Building a SharePoint Online chat room with SignalR and Azure**

 1. Create the SharePoint Online app and associated website

    http://blog.jonathanhuss.com/building-a-sharepoint-online-chat-room-with-signalr-and-azure-part-1-create-the-sharepoint-online-app-and-associated-website
 2. Test the app in Visual Studio

     http://blog.jonathanhuss.com/building-a-sharepoint-online-chat-room-with-signalr-and-azure-part-2-test-the-app-in-visual-studio/
 
 3. Create the SharePoint Online web part

     http://blog.jonathanhuss.com/building-a-sharepoint-online-chat-room-with-signalr-and-azure-part-3-create-the-sharepoint-online-web-part/

 4. Deploy the site to Azure

     http://blog.jonathanhuss.com/building-a-sharepoint-online-chat-room-with-signalr-and-azure-part-4-deploy-the-site-to-azure/

 5. Deploy the app in SharePoint Online

     http://blog.jonathanhuss.com/building-a-sharepoint-online-chat-room-with-signalr-and-azure-part-5-deploy-the-app-in-sharepoint-online/

 6. Gotchas and Thoughts

     http://blog.jonathanhuss.com/building-a-sharepoint-online-chat-room-with-signalr-and-azure-part-6-gotchas-and-thoughts/