It is powered by a rechargeable battery, or you can plug it in to the mains - they all come with adaptors.
It will have a built in wi-fi card, or a plug -in, that allows it to connect to the internet by picking up the signal, like a television aerial picking up tv channels.
You will need an internet connection at home, and a router - the router broadcasts the signal.
Or be in a wi-fi hotspot where you can connect.
This is a useful site that explains both laptops and wi-fi.
http://computer.howstuffworks.com/laptop7.htm