Scan the QR Code
The above page will have a QR Code. You need to scan this QR Code. Steps to take for scanning the QR Code depends on your mobile OS and is shown on that page. For me it was Android and steps were simply to open Whatsapp >> Menu >> WhatsApp Web and scan.
Thats it ! Please note that all messages still lives in your mobile device and your mobile phone needs to remain connected to internet for the WhatsApp Webapp to work as it only mirrors conversation / messages from your mobile device. Secondly this is not supported for iPhone users till now because of Apple limitations, another reason you should switch to Android Phone !