Our dog is a 14 year old yellow lab. His back legs give out and they have begun to give out on him. His "poop" is very dry and just seems to fall

I am curious about his tail tone. My two big concerns would be something called lumbosacral disease (aka cauda equina syndrome) and degenerative myelopathy. In any case, I always recommend a physical exam by a veterinarian. You probably are not going to be able to measurably change these symptoms, because they sound more neurologic than musculoskeletal, but medication may be helpful. Only a vet doing an exam could help answer this. You might be shocked though, how much improvement you could get with an NSAID if this is a musculoskeletal issues (ie. hips)
So before considering euthanasia, have an exam done to determine that nothing further can be done. Again, some of these things could be very simple and comparatively inexpensive.
If nothing can be done, you WILL know when it is time. Watch the dogs eyes for change in facial expression, monitor appetite and know that dogs DO NOT manifest pain usually by vocalization. So just because the dog is not crying out doesnt mean she/he is not in pain. Laying around for a 14 yr old dog is ok, but if the dog's quality of life is in question, I recommend euthanasia.