You can start by searching for an answer to this question on this very subreddit, because it offers one:

Go to My Computer -> The current windows install drive (normally C://) and look for a folder named "$Windows ~BT."

If this is present, once finished this file should be anywhere from 3 to 6.5 GB. Grab your ticket and board the Windows 10 hype train. Windows 10 is ready for launch.

If it is not, all is not lost. Go back up to the C:// drive, (or equivalent), -> Windows -> Software Distribution -> Download.

If there is a folder named "Install," then Windows 10 is currently downloading onto your computer and should move and create $Windows ~BT soon enough. (The hype train isn't quite ready, but is instead just at the maintenance station taking on coal and water, and loading the catering carriage with a nice range of cakes and teas.)

If neither of these options yield results, manually check for a windows update. You should receive a very small update (that does not require restarting).

(side note, I think it is KB2952664 for Windows 7, and KB2976978 for Windows 8 (Windows 8 credit to /u/Chigzy)) Please don't force install them if they aren't in Windows Update and you are downloading just fine.

In my case, this immediately set off the download process.

If this does not work, sadly no Windows 10 for you just yet. (Hype train is stuck in traffic somewhere on the Manchester-Leeds-Islington line, but a replacement bus service is on it's way.)