How do I shut down my new MacBook Air 2024?

You can just let is Sleep by closing the lid.

To completely shut down, use Apple menu > Shut Down and then wait for it to completely shut down before closing the lid.

Also see the information in Shut down or restart your Mac - Apple Support

In addition to @FoxFifth's excellent advice....If you just sleep the laptop all the time, then every once in a while I would restart the computer if you haven't had to restart it to install any OS update patches. Once a month is usually fine unless you find the computer becoming sluggish or you notice any other odd behavior. Some people may go several months before restarting. It all depends on how you use the computer & how it behaves.