<p>I want to check whether the user is viewing my site from a mobile device or PC. If it's a mobile device, I want to redirect my site URL like Google does...</p>

<p>If possible I would like to implement this in JavaScript. How can I do this?</p>

You typically use the User-Agent header to detect the browser.
Here's JavaScript code that does basically that (only for mainstream browsers though, you'd have to add the Mobile User-Agents)
http://www.quirksmode.org/js/detect.html
And here's a list of mobile browser identifiers
http://www.zytrax.com/tech/web/mobile_ids.html
The list is not complete and will never be, given the rate new mobiles appear on the market, but what I did back when I did it is to store all received user agents in a database, and then look for them to classify them as mobile and which brand/model.
What you can't rely on though is JavaScript, it's better done in server code (not all mobile browsers execute JavaScript).
There is a related question here on SO but I couldn't find it.