Can only answer for Sweden. It's usually taken to some regional processing place, where plastic covers and less valuable stuff is removed (ideally also for recycling but probably mostly being burned). It's then sorted, with the extra nasty stuff (like mercury valves, anything of risk containing asbestos or PCB) being removed and handled to dangerous waste processing. Steel parts are sent for steel recycling.
Circuit boards, cables, electric motors and anything with non-ferrous metals is sent to a big smelter facility (once I saw a whole train loaded with seemingly old landline telephone parts). Here copper, silver, gold and other metals are extracted by electrolysis and other processes.
It's not perfect, but it at lest helps reducing the amount of mining needed.