Connecting your Arduino to the internet is cool, but it’s even cooler to connect over WiFi. Luca explains how to connect your Arduino Ethernet shield to a cheap WiFi router to give it WiFi access.
Sometimes however it could be easier (and maybe cheaper!) to connect an Arduino to the Wi-fi network using your ethernet shield in conjunction with a wireless router.
I found the TL-WR702N nano router by TP-LINK that, with a cost of about 20€ on eBay, can work also as a wireless client: in this mode the router acts like a “bridge” between the device connected to its ethernet port and a Wi-fi network.