Getting a finished layout from the Web Switch Builder onto the zencontrol touch switch app (Switch 2) is a manual process, done once the design is saved.
Before you start: save the layout as a .zen file (see Saving, opening and auto-save) and check it in Preview (see Previewing and testing your design).
Put the saved .zen file somewhere the Android device running the app can browse to. Any of these works:
Google Drive
Email, with the file saved from the attachment
A USB cable from your computer
Open the Switch 2 app. On first open it shows its settings page. Launch Switch 2 stays greyed out until a project is loaded.
Under Project, tap Import Project (1). The device's file browser opens.
Browse to the .zen file and select it.
Check that the file name now shows under Import Project, for example Loaded: New_project (1).
Tap Launch Switch 2 (2). The app boots into your project.