If you just want to run js in a page there is http://electron.atom.io/docs/api/web-contents/#webcontentsexecutejavascriptcode-usergesture-callback
However if you want to read some information or get a result you need to use ipc. Example here of using ipc with executeJavaScript together: https://discuss.atom.io/t/how-to-return-value-from-webcontents-executejavascript/22726/9
There's a small helper module for this too: https://github.com/joshwnj/electron-run-in-browser
When creating a BrowserWindow you can specify a js file in the webPreferences.preload option: http://electron.atom.io/docs/api/browser-window/
This file is run before any js, and has access to the electron API so you can set up communication over ipc.