There are lots of videos, but they all use V70s. The 850 does not need to have the glove box removed.
Either lower the coolant level by draining the engine, or, clamp the two hoses that go through the firewall. No need to spill a gallon of coolant inside the car.
Both kick panels come out and tossed in the back seat. The black panel behind the carpet that covers the empty center dash space gets popped our and slides rearward to free up and come out.
Get a small supermarket bag that doesn't have holes in it to catch any antifreeze that will drip out. Remove the T25 screws that hold the plastic shell together. Remove the single T25 that holds the core to the piping that goes to the firewall. Remove the O rings. Remove the core with the plastic bag.
Take off the housing on the old core and put it on the new core, if not supplied. Put O rings on the metal piping. Slide the new core up and in. Connect the pipes with the T25.
Take off the hose clamps to the firewall. Start the engine and let it warm up until the engine fan kicks in, leave the cabin blower off to speed up the process. Turn the engine off and inspect the bottom of the heater core for leaks. Put everything back on, done.
If you like a slow show, this is pretty good:
http://www.bing.com/videos/search?q=volvo+850+heater+core+removal&FORM=VIRE3#view=detail&mid=DD54C877BB25102D596EDD54C877BB25102D596E
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