What is the easiest way to remove bones from a soup or stew? Sometimes I stew meat (various wild game) that results in lots of tiny bones, which becomes annoying to deal with when eating.
Don’t stew the backbone. Cut it out. That will eliminate about half the bone-picking.
I gave up on making chicken soup from a whole chicken because the deboning step took forever and inevitably left some behind. I now use whole skin/bone breasts, and if I can get a small package, about one-third whole thighs to deepen the flavor. If I catch the parts at just the right time, I can debone them in five minutes with nothing missed.
You might not have that option with small game, but anything you can cut off or debone in advance will help. Once you have a pot full of separated bones, it’s a tedious mess.
You can debone the meat first, then put the bones in a cloth bag to stew so you get the boney goodness. If you’re especially picky, once it’s done you can go through the bag and pull out the meat you missed while boning.
Huh-huh! Huh-huh! That wuz cool, Butt-Head! Huh-huh! Huh-huh! 
(Sorry, I just couldn’t resist!)
I just use a slotted spoon. I WANT to cook with the bones, for the flavor, but getting them out hasn’t seemed any more a chore than skimming the grease.
Seriously…
I would brown the meat first in the oven with the bones in. Then I’d separate the meat from the bones as best I could, set it aside, and brown the bones in the oven until the marrow was soft. Then I’d add boiling water to the pot and simmer the bones until the broth was thick and brown. Finally, I’d fish the bones out of the broth, trim off any meat that’s left on them, and put all of the meat back into the pot along with the other ingredients.
It takes a while, but it’s well worth it. Whenever I roast a leg of lamb, I do this with the bones and drippings and make 5–6 litres of strong broth that I put into Mason jars and store in the fridge.
My technique is to simmer the soup until the chunks are just starting to fall apart. I turn off the heat and use a big slotted spoon to lift each one into a big glass baking dish. Using two forks, I push bones, cartilage, skin etc. one direction and the meat the other. Repeat with each chunk. I sometimes have to stop and spoon the discards into the garbage to make room.
Keep sifting the broth with the slotted spoon (tilt the pan if you can) until you’re coming up with nothing but things you want to remain behind.
Then go back through the meat with the forks, both shredding it and finding the bits of bone you missed. Dump the discards and put the meat back in the pot.
Cheesecloth bag.