In reply to mypyrex: As well as tethering over wifi you might want to try tethering over bluetooth:
http://www.scaine.net/site/2013/01/android-to-android-tethering-over-blueto...
This is how I surf from my wifi-only tablet via my Xperia phone. The tablet is running Cyanogenmod 10.2 (Android 4.3 Jelly Bean), the phone is running the stock Sony firmware (Android 4.1.2 Jelly Bean).
In theory my mobile tariff doesn't allow tethering - if I try to set the phone up as a wifi hotspot, the tablet can connect but it doesn't get access to the Internet. Using bluetooth tethering, the tablet connects to the Internet just fine.
I suspect that the bluetooth tether is less battery-hungry than the wifi hotspot, though I'm not 100% certain of that. It does means that my phone is not advertising a wifi network to all and sundry - some client sites that I visit do not allow wifi hotspots at all, but are OK with bluetooth.