Say I have a #6/3 cable being spliced in a metal junction box. How would the (presumably stranded #8) ground wire be connected to the box?
You can connect in much the same way you connect anything else. The only difference is the size of the wire nut. Something like a B-cap B4 Blue would do it, or you can just go with a small split bolt connector if you feel the wirenut would be over capacity.
By the way you don't use a #8 to the box since this is a bond not a grounding conductor. A #10 would be good for a 60A circuit if that is what the #6 is for. To bond to the box you could pigtail and attach to the box with a standard grounding screw (green) and use a crimp connector (spade, loop or some such).
NEC Table 250.122 Minimum size equipment grounding conductor. You size it off of the overcurrent Device. If you feel like doing some more reading you can go to 250 Part 5 Methods of equipment grounding which will refer you to 250.30(A)(1) and on and on and on. The gist of it is go to Table 250.122 and size it from there.
I would go with classic crimp ring terminals. Mind you, these can be stacked 2 or higher on a ground screw.