How do I/can I install a dimmer without a ground?
A dimmer that buzzes is using an obsolete way to dim. It's also buzzing all your surge suppressors and the AM radio for half the neighborhood.  

Grounds are not used in any way whatsoever as part of the functioning circuit.  Electrons should never move on a ground path.  So the dimmer shouldn't need it to function, but a newer, better dimmer might need a neutral wire.  Make sure you are considering future LEDs when picking a dimmer.  The better LEDs (GE, Cree) are really quite good now, and it's time to say goodbye to incandescents. 

I do see a ground wire back in there.  It also looks like a steel junction box.  It is likely the ground wire is either strapped to the box (typically with a #10-32 screw) or is otherwise attachable with a wire nut, possibly already attached to other wires. 

You also see the metal yoke on the switch.  That is meant to be ground.  You see where the yoke is resting on plaster, not the steel box itself, so the ground path there is weak - depending on the metal screw.  Because of that, I'd use a wired connection of bare (or bareD) wire to go from an attachment point to the ground screw on the switch.  

By the way, that little paper square on the bottom of the box, is designed to go on the screws on the switch yoke.  You slide or screw it onto the screw, and now it will stay captive and not fall out.  Sometimes they get unscrewed by accident as you're removing the switch.