As in love with Linux as you'll be, you're eventually going to have to force yourself to turn it off at some point. There are two levels of quitting a Linux System; one is to Log Out, to prevent someone from getting into your account and messing anything up, and the other is to Shut Down.
To Log out, move to the upper right corner of the screen and click your name in the top right corner. Near the bottom of the menu that appears, notice the options to Lock Screen, Log Out, or Suspend. They're all similar and all end up making it so that in order to use your computer later, you'll have to enter a password.
If you Log out, you'll be taken back to the main login screen. If you Lock the screen, the screen will go black and to get back in you'll be asked for a password. If you suspend, the computer will go to sleep, an extreme low power mode, and when you "awaken" it again, you'll need to enter your password.
From the login screen, you can shut the computer off by going to the same place (top right corner) and selecting Shut Down.
Linux has lots of ways of doing things. Shutting down is no exception. If you know you want to shut down and don't want to bother logging out first, it's fine to do that. And the way you do it is to hold the alt key down as you log out. Instead of Suspend, you'll see Power Off... which will indeed safely power your computer down.
Time to level up! You're an expert on the Linux Desktop now. Wasn't that fast? Don't stop now. Continue on to the next lesson!