If I have a mobile phone using 3G could I connect my laptop to the internet by "piggybacking" the phone? Essentially using the phone as a wi-fi hotspot.
Yes. it's called tethering.Have a look here:https://www.google.co.uk/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=tether%20mobile%20to%20laptop