I'm so sorry you're going through this. I very unexpectedly had to put my dog to sleep on Tuesday. He was my best friend for 15 years (I'm 24). I do not know how to live without my dog. I am not really coping (and it's okay).
You need people with you; don't do this alone. Without my partner I probably would have just lay in my bed until I died, too. He helped me take the excess dog food from the house and donate it to the RSPCA, he took a few days off work to help me pack things up that were just too painful for me to look at right now, he's making sure I eat, and he holds me when I cry and allows me to grieve. It would have consumed me totally without his help.
My manager at work is a close friend who organised me to have the week off when she heard what was happening. I'm glad, because I am still in no shape to work. Do you have any obligations from which you might need reprieve? Are you able to let them know what's going on?
Thus far, I have made it through to today when I saw my psych who compared my loss to when he lost his father, emphasising/validating the loss I've suffered. Don't downplay your loss, and don't listen to people who want to try to. Don't argue with them, just leave the conversation; it's not worth the effort.
I had one last day with my boy, and it was wonderful and kinda terrible. We spent the whole day cuddling and went for a little walk, but I felt like we were just waiting for him to die. Let yourself feel whatever feelings crop up.
When it's time, it will be hard and it's okay. Just hold your dog, tell them how much you love them. Even if you're sobbing uncontrollably, please be there with your dog in his final moments.
If it's possible, have the grave dug in advance if you're burying your dog. I regret not having that organised. Again, I had help because all I could do was sob.
I feel like I will never be happy again, but it will get easier I'm told; it has to. Be kind to yourself, and please, please reach out to friends/family who can help you get through this. Grief groups or seeing a psychologist to help you through this are great resources to help you navigate this grief.
tl;dr: * Don't do this alone. * Don't downplay how big a loss this is. * Let your boss/other obligations you may miss know what's going on. * Reach out to others.