I too was nervous about the download, as this is my first digital game to download and I wanted it to work. Here's what worked for me and it should work for you too.
1. After you've bought the game and have your product code, Google for EA Download Manager. Download it. This is EA official downloader, similar to Valve.
2. Once you've installed and completely setup the EA Download Manager, you get to your first screen where you see a little sprocket icon next to your profile picture on the left side. You'll see an option for redeeming your game code. This is where you will put the product code in. Choose which version you want to download (I got the option to download the digital deluxe version)