Most of my pets died due to complications of old age.
I think the best thing a person can do, is be honest with yourself when it finally comes time to put an older animal asleep. So many people, I think, wait way too long because they just can't let go of their long time companions.
In the meantime, just remember that going/being blind or deaf, or both isn't painful for the animal and they can learn to adjust to it and still lead a happy life.
A touch of arthritis can be controlled with meds that your vet can recommend. Also remember that dogs and cats will often hide signs of pain, so keep a very close eye on the way your pet moves, especially those first few steps after they get up from laying down for a bit. If you see any odd hitches in their gait or an unsteadiness, it might be that they are experiencing a little bit of pain. Again, have your vet check it out. I had my 19 year old cat get x-rays just so my vet could look at her joints and determine how bad her joint pain might be. It turned out that she only had 1 hip joint that was kind of bad and the rest were ok. But due to the 1 hip, we put my cat on some meds to ease any pain from the bad hip.
Just by looking at my cat it was hard to tell she had a bad hip, she did a good job of hiding the pain.
As mentioned, with the stairs, you might have to start picking up your dog and helping out there. Also, if your dog sleeps on your bed...it might be time to get it it's own bed so your dog doesn't get jostled or try to jump off the bed during the night. I had a little dog that always slept on my bed, but as she aged, I switched her over to her own doggy bed that was next to my own bed. She was very happy with that arrangement....plus I didn't have to worry about her trying to jump down and getting hurt.
Learn to use hand signals if your dog is going deaf, and if blind (or both) sometimes vibrations help...you can clap loudly or stomp a foot to get their attention. And as someone already mentioned...keep their walking paths in your home free of obstacles...don't leave shoes, or socks or books anywhere your dog might walk and trip over them because they can't see them.
Anyway, as I said, I had a lot of elderly pets in my life and I think that one just has to monitor them more closely, see if they are eating less, or walking oddly sometimes...things like that and then find out why by having the vet check them out.
Stormy
