Here is a photo of some CGI crystals with a very nice material. How can I achieve the somewhat foggy, fractured, etc. effect inside the crystal? I assume some sort of volume node with masks or something?
first: good illumination! there’s not so much fancy effects in this scene (glass with bumps!!)… but if you want, get good textures for normals and volumetrics, and a simple glass shader+volume scatter+volume absorbtion should give you something more realistic and heavier to render 
What type of texture would I even use for those sharp planes? Just random triangles and such of different shapes?
not testing it right now, but I’d try geometric texture mixed with some low level noise as ‘normals’ for the refraction shader and an almost clean surface for the reflections.
Your image shows a lot of effort in scene lightning and post effect glows! The shaders look in fact pretty simple.
Take a look at this tutorial. It deals with ice but the technique could easily be adapted to do crystals like in your image.