You need to use the API under window.safe*, look at the complete documentation here: http://docs.maidsafe.net/beaker-plugin-safe-app, and the webFetch function is documented here: http://docs.maidsafe.net/beaker-plugin-safe-app/#windowsafeappwebfetch
You can take a look at the snippets to understand how to connect to the network here in this doc: SAFE Network API - Getting started (draft)
E.g., you can do something like this after you connected to the network (for browsing the web you don’t need to authorise you app, just initialise the library with window.safeApp.initialise and then connect with window.safeApp.connect):
window.safeApp.webFetch(
appToken, // the app token obtained when invoking `initialise`
'safe://nebnotes.arsnebula/locales/en.json' // the SAFE Network URL
)
.then((data) => {
console.log('Web page content retrieved: ', data.toString());
});