How do I update elementary OS when new versions come out? Is there a setting that does it? Is it Software and Updates that does that? I know it does apps but, I wasn't sure about the OS.
For the moment is impossible to upgrade from one version to other, the problem is that they are based in the LTS versions of ubuntu and you can't upgrade from LTS to LTS, I don't know if the elementary team is working in something to solve this problem in the future, but for the moment is not possible to upgrade the system from one release to other directly. One thing you can do is have you "Home" folder in a separated partition, so every time you reinstall the system your files and config are preserved.
I guess the process is simiar to debian, see: https://www.youtube.com/watch?v=Kg8CSdc0YAA
just have to edit the entries in the files contained in /etc/apt/
replacing with the ones related to the newer Ubuntu LTS