Today, The Witcher 3 has got a couple more of the sixteen planned bits of freebie DLC; a new mission and a different outfit for Yennefer. That’s all fine and dandy, but actually installing and activating these DLC bits through GOG Galaxy is a bit convoluted (it is still in beta, after all.)
Since I only just figured it out, I’m going to assume others might be in the same situation. Here’s a short guide.
First of all, make sure you’re actually signed up for the free Witcher 3 DLC to begin with. On GOG Galaxy’s Witcher 3 page you should see a $0.00 ‘Free DLC Program’ offering under ‘Additional Content’ (not the expansion pass, that one costs money.) ‘Buy’ this free package through the checkout process.
To actually install and activate these things in the game, click the ‘More’ tab on the game page (as shown below) and go to ‘Backup & Extras.’
This should give you a big ol’ list of extras down the right-hand side of the page. Find the DLC offerings in the list (new mission, extra haircuts for Geralt and the like) and click on each one to download them. If you get a weird ‘Disk access error’ message for any of them (like I did,) just try again and it should eventually go through.
That seems like it should be the final stage, but actually it isn’t. Over on the dark grey left-hand side of GOG Galaxy, where you now have a little list of the recently downloaded Witcher 3 DLC bits, hover over one of them and find the spy-glass icon. Click that to be taken to a local folder with your various DLC .exe files in it. Yes, you need to install each one manually from here.
Do that, and the DLC should finally be active in the game next time you load up. If you want to mix and match, the ‘Configure’ drop-down tab (as also shown in the image above) should let you toggle the installed DLC with checkboxes.
If you have your user.settings file on “read only” (due to tweaks,) the DLC won’t activate properly. Disable “read only” (and do a backup of the file if you’re nervous about your custom settings) before installing.
Edit 28 May: Judging by some of the comments below it seems like I was making this harder than it needed to be. According to reader Anbear, you can go straight to the ‘Configure’ menu and check the DLC boxes you require to get them to download and install. That would, indeed, be a bit easier.