It's easy: you don't need to do anything. 🙂
All your games are tied to your Origin account. As a result, you can keep on your games, you simply need to install Origin on your new computer ( download it from: http://www.origin.com/download) and log back in with your account info.
You'll then be able to download your games right from your Origin games tab in the Origin client.
If you have any more questions, feel free to ask .🙂
