The question says it all. Basically, I just want to know the alternative for this in WinRT:
Process.Start(\"http://www.google.com/\");
In WinRT, you can use Windows.System.Launcher.LaunchUriAsync to launch the default app associated with the specified URI.  For a web link, the default browser would be used.
MSDN: Launcher.LaunchUriAsync(Uri) | launchUriAsync(Uri) method
You can use Windows.System.Launcher to launch files and URL's...
Windows.System.Launcher.LaunchUriAsync(Uri) will launch a given Uri with the default application. If it's a link it will open with default web browser. You can use file:/// scheme to open an network resource, but not resources on the local file system.
Windows.System.Launcher.LaunchFileAsync(IStorageFile) will launch the default application for the given file.
Both that methods has an optional second parameter of type Windows.System.LauncherOptions that customizes the launch.