Assuming a Windows laptop, set up Internet Connection Sharing on the Wi-Fi interface, choosing the Ethernet interface as the home networking connection. Then, connect the OBi to the laptop's Ethernet port. You might need to use a crossover cable (if the Ethernet connection status shows "media cable disconnected", you do). If you have Wi-Fi at home, you can test this without going to the library.
However, why do you want to do all this? Wouldn't it be simpler to just plug a headset into your laptop and use a softphone?