Actually,you asked this at a really good time for me, as my last dog died just yesterday (or the day before - but I found out about it yesterday).
When I lived at home, we had three dogs - Giz the Yorkie, Mac the Westie, and Lobo the Samoyed. Giz died about 6 years ago. 5 years ago, I left home (Wales) and moved to the USA. Earlier this year, Lobo died. Not long after that, I went home to visit for the first time, where Mac was the only surviving dog. Yesterday I got a message on Facebook from my father that he'd died the previous day.
The first thing that happened was that I cried. Not loudly, silently. And as I cried, I wrote a reply to my parents. I thanked them for telling me, and told them that, whilst I wasn't expecting it, I also wasn't particularly surprised. I told them that, by the time we spoke on the phone this Sunday (I always talk to them Sunday afternoon), I'd have processed it more and would be okay.
Then I told my wife what had happened. I told her that I was sad, and I was - I was crying, and speaking was difficult. But I verbally mapped out the whole process. I told her that I'd swing between 'not thinking about it' and 'mourning and being depressed' all week. Then, by Sunday, I'd feel as though I was over it altogether. Then I'd talk to my parents, and discussing it with them would give me new information (such as how did they find him, where, what did they do with him afterwards, what was the last thing he did, etc) that would open the old wounds, and I'd break down again. Then we'd reminisce, I'd be depressed for a while, and gradually I'd go on with my life. It was the same for Lobo, and even for my grandad, who died last year (I have a lot of guilt over that, but that's a different issue).
Basically, knowing ahead of time how I'm going to react helps me when it comes. Emotions are inevitable and uncontrollable - I won't be able to prevent breaking down when we discuss it - however, knowing about it in advance makes it easier, as it's more like going through the motions. It also helps that I went through a similar situation recently, with Lobo, so it's still relatively fresh.
The truth is, I'm more worried about my mother. Now, for the first time, she will come home from work, and I won't be there, dad won't be home yet, and now there won't be any noisy dogs to greet her and require walking and feeding, either. For the first time, she's going to be truly alone. She already had empty nest syndrome before - I'm worried that this will drive it home, hard.
Thanks for making this thread - I was going to make a similar one myself, actually, so the timing works really well.

And don't get me wrong, I AM sad about Mac - he was there all through my adolescence - so I'm very sad, I've cried, and I will mourn and cry more, but being analytical and knowing why I'm emotional makes it easier to deal with. I try to deal with death in the best way I can.