You're right -- there is no "Devices" menu (and if iTunes Help says there is, that is indeed a gaffe on Apple's part). Launch the iTunes application. When iTunes opens, connect the Shuffle. After a few seconds, a new section named "Devices" should appear in the column at the left side of the iTunes window. It will p'bly be in an expanded state (the wee, gray "disclosure triangle" pointing downwards), and below the Devices label will be an icon representing your Shuffle. (If the disclosure triangle isn't pointing downwards, click it to open the Devices section.)
Click on the Shuffle icon to select it. The right side of the iTunes windows will display the Shuffle's "Sync Settings." Now I'll just quote from iTunes Help (this comes an older version of iTunes than you're p'bly using, so this may not exactly match the info in your Help window):
• Click the Music tab, and then select “Sync music.” (i.e. put a checkmark in the Sync Music box)
• Choose “Entire music library,” or choose “Selected playlists, artists, and genres” and then select the playlists, artists, and genres you want to sync.
• To have iTunes fill any remaining space on your iPod shuffle, select “Automatically fill free space with songs.”
• Click the Sync button.
When the sync is completed, click the small "Eject" icon to the right of the Shuffle's icon in the iTunes window; this will close the file system and remove the Shuffle from the USB bus. Disconnect the cable at your leisure.
If you want more detailed info, visit this Apple support page on
Syncing music to iPod shuffle. (Covers all 4 "generations" of Shuffles, with illustrations.)
If the Shuffle doesn't appear in the Devices section, or if the Devices section doesn't appear in the left side of the iTunes window, then there's a problem...could be a bad cord, a bad USB port, a missing piece of iTunes software (very rare on a Mac), or the Shuffle itself is wonky. If that's the case, post again and folks will help pin down the problem.
Should I just throw both iPod and computer out the window?
Well, if your window is next door to my house, please do; I'm always happy to get another Mac ;-)