In this thread, i see three different things mixed up
1) connect the company's intranet
This step is the hardest as it depends heavily on the security your company applies. Solutions range from simple userID/password schemes, over more complex VPN configs with or without certficates upto to special security apps generating one-time tokens.
2) once being connected to the intranet, getting Access to files on Windows fileservers
This is the rather easy part: there are several apps to browse files on an AD file share, one example was already mentioned above: "Filebrowser". Search for it in the AppStore.
3) being connected to the company's intranet trying to access the outside world aka Internet (gmail, Apple store...)
As in 1) this heavily depends on the Security setting your company's network administrator applies. To get from the Intranet to the Internet most probably you have to pass through a FW. A HTTP proxy helps in doing so. In most cases a manual HTTP proxy config with the right authentication credentials will do the job. For details in your Intranet environment get in contact with your network admin. In certain situations it might even be, that getting out is simply forbidden: Eg I had the case when dialing in to the intranet from the internet via VPN going out again was forbidden, simply due to bandwidth (tromboning) reasons. In those cases just close the VPN and you're on the Internet.