What's the best way to update a site after going live?

I am going to be going live with my website soon. As of now I simply trial and error my way into updates and fixes but this isn't going to work after launch.

I'm guessing the best way is to host a complete duplicate of the site in a hidden sub-folder and work with that. Updates and feature builds can be done to the duplicate and after testing I can replace the live site with the updated copy.

I'm not a tech guy so I'm just wondering what people have found to be the best method for this.

Thanks!