If you use a Tesco international calling card your outgoing call will cost you 2p per minute to the USA (plus a 4p connection charge), for calling both landlines and mobiles. If you're calling to a person using a US-based phone service (either landline or mobile) they won't pay anything for the incoming call. Otherwise they'll pay the charges set by their UK (or other) provider. Those charges can be very expensive. (For example Vodafone charge 99p per minute at their standard rate or 75p per minute with their 'International Call Saver' service).
If the person travelling to the USA has a phone which is unlocked to all networks they could buy a SIM card in the USA, thus getting rid of the charges for receiving incoming calls.
Alternatively the person travelling to the USA could buy an international calling card when they get there, allowing them to make cheap calls back to the UK.
It should be remembered that most UK mobile phones won't work in the USA. Only quad-band (or possibly some tri-band) phones will work there.
Chris