Eduroam is a wireless network that is available in universities throughout Britain, widely across Europe, and in some places in the rest of the world. It accepts logins of any member institution - so, for instance, the OUCS Remote Access login can be used for the Eduroam network wherever you may be. Once set up, your laptop, iPhone, or whatever, will connect to the Internet with no further action if an Eduroam wireless signal is detected.
Eduroam is just another wireless network. If it is visible in the list of wireless networks which you can get through the wireless icon (the way there varies according to the version of Windows and the make of the wireless card in your laptop), then you can simply tell your laptop to connect. It should then ask for:
The username is your OUCS username, with @ox.ac.uk appended to it, for example: CLPH9876@ox.ac.uk
The password is your OUCS Remote Access account password (not your SSO password).
If you do not currently have an OUCS Remote Access account set up, then follow the guidance given here to get one set up.
Once you have connected to Eduroam, you are connected to the Internet. You are not connected either to the Oxford University network, nor to the network of the institution you are visiting. Just like at home, really.
So, to connect to the office, you need to activate the VPN in the usual way.