OK, crapping myself now. Just bought an Xbox One for DS (13) for Christmas. Why does downloading games take so long?
It depends on the size of the game, and whether you've purchased a disc copy or digital copy.
If you've bought a disc copy, you may need (or want) to install it - it sometimes makes things run a little smoother. Many games also end up being 'patched', where bugs and issues are retrospectively fixed after launch. This can take ages, it completely depends on the nature of the fix. For example, the new Final Fantasy game had a day one patch was was pretty hefty. You can set up the consoles to background download updates.
Digital copies require you to download the entire game and any patches/updates.
You may want to set it up beforehand, because the console's firmware gets updated on a regular basis too. Leave it to Christmas day, and you could end up spending a few hours updating the console itself, followed by updating games.
(Also I've only skimmed the thread, so this has probably been mentioned, but make sure you have any parental controls for content and online purchasing set up - my brother failed to do this a few years back and my nephew blew £400 on Fifa and Call of Duty DLC !)