Populous: The Beginning has been extensively tested and is compatible with Windows 7, 8 and 10. It is also compatible with Windows Vista. It works perfectly, as long as these instructions are followed.
The installer that comes with the original version of the game may not work. Fixing garbled colors requires either a registry fix or using a program like DxWnd. But none of this is required if you download a compatible version. You can install the compatible version even if you already have the game installed.
The Direct3D version of the game may not work with Windows 8 (and does not work with certain newer video cards in other OSes), but the Software version should work perfectly. The Direct3D version has only very minor graphical improvements over the Software version.
The game’s resolutions available by default are good enough to play, though you may choose a higher one if you wish. This requires running the game with the /allres parameter, and then changing the resolution in the options menu.
Download Populous: The Beginning (~20MB) bundled in with fixes for these operating systems and ready for singleplayer and online play.