I had the same thought as Phil. I shutdown the droplet and took a snapshot. My mental model tells me that I should now need to boot the droplet. This is not true. It automatically restarted after the snapshot. It doesn't help that the next thing we see is the "We recommend rebooting from the command line" message.
If you're seeing that message, then the server is on. Above the 'Power' tab, you should see the server IP and status 'Active.'
sudo shutdown -h now;
sudo reboot now.
Would be useful if DO would link to the article how you can power down a Droplet from the command line. Seems to be
sudo shutdown -hP now. I did and could no longer ssh into box. But I did not see status powered down from the DO Dashboard. Took a snapshot anyways. And then was told this can take up to an hour. Waited for about 5-10 minutes for it to be done. Basic Ubuntu 16.0.4 box running NGINX, PHP and MariaDB and one bare WordPress site. After snapshot was done I could immediately ssh into box. Not sure yet how I can verify the snapshot is functional or not.