There are two versions of the Kindle. The cheaper one only connects to the internet by receiving a signal from a router. (i.e. by 'Wi-fi') Since your friend obviously hasn't got one in her house, she'd need to go to somewhere with free wi-fi (such as Costa) in order to make the connection.
http://www.amazon.co.uk/dp/B002Y27P46
However the dearer version of the Kindle can also connect to the internet via the 3G mobile phone network, free of charge (and in over 100 countries). That would probably be the best product for your friend.
http://www.amazon.co.uk/dp/B002LVUWFE
Chris