I think the grieving stops and the pain fades- never completely goes away, but does fade.
I've never owned a dog before Blue, but I did have a cat growing up. When he passed, I couldn't believe the pain I felt. It lasted for a long time too.
I know many people get another pet and it helps with the pain a lot. Thinking back, I wish I would have done just that, get another pet. Looking after a new dog/cat limits the time you dwell on the one you lost. At least I think so. Again, I'm not saying the pain goes away completely, but it becomes bearable. And eventually, you can think of them and smile, instead of cry.