Wi-Fi can be used if:
[LIST=1][*]You are in a wi-fi hotspot (wi-fi is not a universally available thing .... it's not something you can just use anywhere. Someone, somewhere needs to be running the wireless network.)[*]It's a public - ie. un-protected - wi-fi hotspot[*]It's a protected wi-fi hotspot that you know the password for[/LIST]
Typically, a router is used in people homes. If you think of the wi-fi broadcast as being a "bubble" around the router (albeit, an invisible, wireless bubble). If you are within that bubble, you can access the wireless network.
Leave the "bubble" though, and you lose the signal.
Public wi-fi hotspots may be bigger, but they may only offer slow connection speeds. You should alse be careful what you acces if using a public/un-protected wireless connection. I wouldn't be using it do any online banking or anything like that!