All data stored is exposed at /data and can be requested using plain HTTP. GOG DB uses plain JSON files, sometimes gziped, to store data and an SQLite index for faster load times and they're all in that directory. If you want to operate on the full dataset, either use the index file or download a dump from /backups_v3. 100 small requests already generate a lot more server load than a single big one, so please use the backup downloads whenever possible. There is no documentation, read the source code to figure out what something means or ask me directly.
Please don't! All the collected data is available in machine readable JSON format, see "Is there a GOG DB API?". There is no hidden data that is only accessible through the website, so you would only be wasting server resources.
The userscript is available at gogdb.user.js. It automatically adds a GOG DB button to every store page. You need an addon like Greasemonkey (Firefox) to install it. Once the addon is active click the link and a dialog to install the userscript should open.
GOG DB uses the following GOG API calls to collect its data:
https://www.gog.com/games/ajax/filtered?mediaType=game&page={page_num}&sort=popularity
https://api.gog.com/products/prices?ids={ids_str}&countryCode={country_code}
https://api.gog.com/products/{prod_id}?locale=en_US&expand=downloads,screenshots,videos,changelog
https://api.gog.com/v2/games/{prod_id}?locale=en-US
https://content-system.gog.com/products/{prod_id}/os/{system}/builds?generation=2
https://cdn.gog.com/content-system/v1/manifests/{prod_id}/{system}/{legacy_build_id}/repository.json
https://cdn.gog.com/content-system/v2/meta/{meta_id}
The updater runs every 2 hours starting at 00:45. It takes around 15 minutes to complete.
Probably, feel free to contact me and tell me what you're trying to achieve and I will try my best to help.
If you found bugs or want to request a feature, you can find my contact information on my personal homepage.
Source code is hosted on Github.