I had to go through this in January. It was the hardest thing I've ever had to do. She was 16 years old and my very first pet. 
She wasn't responding anymore and basically didn't really know where she was at all. She was on meds for severe arthritis of her spine and legs. Had lost alot of weight in a matter of weeks. Her legs and body were very weak and she would fall everywhere even in our pool.   
There are many pet lovers at my workplace and I would ask them how will I know when it's time and every single one of them told me the same thing "You will know - she will let you know" I didn't understand what they meant because she wasn't even all there anymore

  Vet had said she was senial. 
I am also a christian so I prayed about it alot and asked God to please help me with this. My prayer was always "Lord please take her naturally in her sleep when it's time"   
Someone told me don't talk to her just look into her eyes and you will know.  
I received a call at work that she wasn't doing good. I rushed home and found her stuck in a corner in the rain. My daughters had been trying to get her in house and she wouldn't stay. I looked at her and started to cry - she looked so thin and lost. 
I remembered what that person had told me so I took her face in my hands and just looked into her eyes without saying a word I just thought it in my mind -" I told her how hard this was for me but that I needed her to let me know because I didn't want her to suffer anymore and I didn't want to be selfish I told her how much we loved her and how special she was to all of us" 
For the first time in a long time she actually looked at me and started to lick my hands and face. There was also this amazing peace in her eyes and then I knew she was telling me it was ok.
 I started to cry and I told her I know sweetie - I know thank you for letting me know - I know you're tired.  
I kissed her and held her for very long time then she turned around and fell asleep. We drove to the vet's office she was still very peaceful when we got there and she went to doggie heaven that night.  I still had very hard time after that but deep down inside I knew I had done the right thing.  
You will know when It's time. They do let us know. 
I hope this helps you - my prayers are with you for strength and peace.