I believe you have to download the Music app from the Market to take advantage of Google Music. Samsung probably replaced the stock music app with a Touchwiz one that doesn't have access to your Google Music account.

 

I haven't tried it with the stock app. I did what TheBlackPrince suggested and downloaded the Google Music app. You have to go into the settings for the app, choose Google Account and select your account (even if you only have one) to get your stuff to show up the first time.

 

This is the correct way. Download the app. Go into it and hit menu. Click on settings and choose your account. It automatically syncs within seconds after that. Sometimes the settings menu won't show when you first install the Google music app. Have to let it sit and then go back into it. That's a bug with the app.