Where are all the Stones of Barenziah located? (No Stone Unturned)

If you have the latest patch, the Thalmor embassy one has been moved so it's not in the bedroom anymore. It has been relocated to the cave after you rescue someone from the Thalmor dungeon.

Knowing where to find each of the Stones is half the battle, but this info can easily be found online, for example in the UESP wiki mentioned by the Accepted answer, or on the Fandom Elder Scrolls wiki.

The harder part is often keeping track of which ones you've already found, because you're basically on your own for this. My wife and I used to use a Google doc to track them, but for multiple playthroughs it gets tedious to reset the list. I ended up building a mobile app (aptly called "Barenziah Tracker") to help with this - it includes location info and screenshots from the Fandom wiki, and lets you check off each stone as you collect it, with independent lists for multiple playthroughs. Here's the link for iOS, and here's the link for Android. Hope that still helps someone enjoy this timeless game.

I recently made a guide that includes all the 24 stones of Barenziah and the final reward. Hope this helps everyone!