Not sure what you mean by "How do I sync my desktop (Win 8) apps to my Surface Pro?"
If you want the same apps on your Surface Pro that you have on your desktop, you need to install those apps on the Surface.
There's no way I know to "sync" them so that if you move around an icon on your desktop's desktop, it would be moved on your Surface; they are two different computers (it's not like syncing iPads with iTunes).
You can use SkyDrive to save files to so they'll be accessible to both. You can use Remote Desktop to see and run one computer from the other when they're both on the same network.
Or you can do what I did, ditch the desktop computer and connect the Surface to your monitor and USB hub when you get home. I got a 27" monitor running 2560x1440, USB mouse and keyboard and several external and portable HDs and flash drives totaling more than 3TB for storage.
The Windows 8/RT sync is personalization-specific for general OS settings (themes, backgrounds, etc.), while the "app sync" aspect is limited to certain specific applications like MS Office. You have to sign in to both devices using your Microsoft account.
I think 8.1 will give you that ability. The other day I installed a fresh copy of WIN8.1 on my ultrabook and when I signed in, all my apps were in the same arrangement on the Start screen as my Acer tablet. So the tiles were there, but did have to redownload all those apps, so all you have to do is tap on the app and the download start.
You need to sign-in on both systems with the same Microsoft Live ID account. This will allow you to synch changes done on one UI to all the other Windows 8.x environments you will subsequently login using the same Live ID account.
The other way is to register all you systems to an Activte Directory Domain and use a roaming Active Directory account. However this is usually beyond most home-based environements.