You need a software to help you back up your games on to discs. However, by backing up and not modding you only make sure that you can play those games later on when the original wears out and you finally get ready to mod your Xbox360. If you are wondering how to play xbox360 backups, well you will absolutely have to mod your xbox360. Fortunately enough, this can be pulled off with some small software modification, which can later on be reversed, if for example you'd like to sell your console.
As for how to backup the games, there are loads of guides on the internet and most of you require to get an iHas drive, which costs a fortune and you will have to mod it and it just makes it a major headache. However, there is a software called [GameBackupSystem] (I personally use it) which takes out most of the process details and makes it a lot shorter. Well worth the 30 bucks I've spent on it. They have also updated recently to support XGD3, I think.