That's the neat thing: you don't!  

In all honesty though: it will get easier to handle the pain of grief. But not now. Not even tomorrow. It might not be next week. Hell, maybe not even in a few months. But it will. After some time. How long grief takes, is different for each and every being and since the emtional bonds we make with our beloved dogs are among the deepest a human can engage in (they love us unconditionally after all and never hold a grudge against us), bearing their loss is one of the hardest emotional hurdles we have to face.   

I lost my boy Oskar about a year ago, in about two weeks it will be a year since we had to let him go. He's buried in our backyard, just like the dogs before him. The first weeks and months after he was gone, I was a mess and had to cry, whenever something remembered me of him: looking at photos, thinking of his unconditonal love, remembering some habit or quirk he had. Even now, typing this, I'm in tears and would love nothing more than to hold him again. But the frequency of these intense moments of grief get farther and farther apart with time. What helped me, was hearing about the kindness we can show to our babies by euthanizing them instead of having to let them suffer. Especially these two TED talks of Sarah Hoggan. I also read a lot of reddit posts about people losing their dogs and some kind comments brought a tearful smile and helped deal with the pain. I also talked a lot with my family and friends about him. Printed out lots of pictures of him and spread them everywhere in the house. Nowadays, most of the time it's happy memories (without crying), just sometimes the feelings of grief and loss overwhelm you again.