There are a few ways to watch the 2012 London Summer Olympics online, but this is how I do it:
Choose your operating system and follow the instructions on the page.
Go to http://www.bbc.co.uk/sport/olympics/2012/live-video and click on the "Live" link.
From here you should be able to choose and watch the live streams of the Olympic games!
I'm not sure how long this method will last, but I hope it works during the duration of the entire 2012 Summer Olympics.