Let's face it, the most important thing on a computer is your data. On Windows, you went to My Computer or My Documents or My Music and these locations opened in Windows Explorer. On Mac OS, you opened the Finder and found your files. On Gnome, you simply launch the Files application (affectionately known as "Nautilus", after the famous submarine piloted by Captain Nemo) and look through all of your data.
Nautilus is fairly straight-forward. In the left panel are bookmarks for important locations. Your default starting point will almost always be Home because that's where all your data lives. You can see the files and folders in your Home in the right panel.
You can use the View menu at the top of Nautilus to change your view. Some people like see the large and hard-to-miss icons but others are used to a list view. There's also a multi-column view, if you prefer.
Even the most organized among us sometimes forgets where a file got saved, sometimes. If you can't find a file, use the search field in the top right of the Nautilus window. Hit the Return key to start the search, and you'll see all the potential results appear in your file list.
Of course Nautilus doesn't just explore files that are directly on your computer. It can also help you manage files on thumbdrives or even on network shares at work or on the internet.
Other locations are available in the left panel of Nautilus; if you have an external drive plugged into your computer then you'll see it listed there. If you have a network shared folder configured, you'll also see it on the left, or you can access the network share via the Go menu at the top of the Nautilus window.
Notice that you can eject harddrives via the left panel, as well.
Network shares will be covered in more detail later.
Practise moving some files around with Nautilus. Remember that you can launch two nautilus windows at once, and drag and drop files from your Downloads folder, for instance, to your Music folder or Documents folder.
Try downloading a file from the web, in Firefox, and look for it in Nautilus.
Try throwing a file you don't need any more into the trash, and then empty the trash. Hints: The trash is located in the left panel of the Nautilus. Look for an Empty button!