Okay, all you need to do it your from the UK is click on the first link then paste the second link in your address bar, then you're done. If you're not from the UK then follow these steps.
Use a UK proxy site like daveproxy.co.uk or goproxing.com.
Go to stardoll.com, then login! Paste the first link into the address bar on the proxy site then hit go, then do the same with the second link then you can log out, and find your free dog in your suite after returning to your normal Stardoll! (without the proxy)
First Link: http://www.stardoll.com/en/contest/view.php?id=510
Second Link: http://www.stardoll.com/en/contest/finish.php?id=510