How do I download my stored information on the iCloud to my new Apple Mac computer?

You will have to sign into iCloud, which is done early in the Mac setup steps. See Set up iCloud on your Mac in Set up iCloud on all your devices

Once your Mac has signed in it will sync with iCloud and download data such as contacts, calendars, photos (if you have iCloud Photos active) and all the other services you see in the graphic Apple provides on that page as an example of a user, which I have added below:

Out of view in this graphic are other services: Safari bookmarks, Find My Mac, News, Stocks, Home, and Siri.