I am so very sorry. It is so, so hard.
I remember exactly how it felt and I will never forget that feeling, knowing that my old labrador needed to be put to sleep that day. I drove back from the vet on that awful Sunday night last November pretty much on autopilot and in shock, even though I had known it was coming for some time. I couldn't function for ages.
Your dog was very much loved and had a lovely life with you. Hold onto that.
I am eight months on now. It has got easier in a learning to live with it sense. I have a box of keepsakes with his collar and lead, and a tuft of his hair that I found wafting out from underneath the sofa just after he had gone (as if he was telling me that he hadn't really left me, I just couldn't see him anymore). I have his ashes in an urn with a nice photograph of him on it and that sits in "his" corner of the living room. Collecting those from the vet a week or so after he had died did help me as I felt as though I was bringing him home, back to his rightful place.
I also have a lovely portrait of him which was painted by a fantastic artist friend. I am so glad I have that, and I am now starting to feel able to ask DH to put it up on the wall for me again the next time he has his drill out.
It feels hellish right now, but get through one day at a time and you will gradually learn to cope. I often find it helps to think of all of the mad things that my labrador ever did, and yes, the naughty ones too. The times he upstaged me! There were plenty of them. I can laugh and smile about them now even tough I do still feel tears stinging a bit.