The new dog we have is terribly constipated. It takes the poor thing at least 10min to poo out a tiny bit. The poor thing strains and strains and almost nothing comes out. I figure the new diet at our house is causing this along with the fact she had surg a month ago. Any tips on things to feed her to soften things up?

Is he getting plenty of fresh water and exercise?
Is their any hair obstructing it from coming out?
Is he in any pain? Crying?

If he is pain, I would take him to the vet, he might have eaten something, but most likely it's because of the surgery.
Did your surgery package say anything about constipation?
First call your vet for advice over the phone, if that doesn't help I would suggest the following. But I'm not the pet expert, she is in Australia and probably sleeping right now.:)

Canned pumpkin (NOT pie filling) just purée pumpkin, depending on his size a couple Tablespoons in his food or a couple teaspoons olive/canola oil.

Thank you! She doesn't cry out so I don't know how painful it is. She is a rescue dog we took in and I am trying to get as much advice as I can.

Lots of water, you can put some peas in her dog food also. Make sure no hair mattes around the outbox
What kind of dog is it? IS it a dachshund, small dogs are prone to digestive problems, some require medication from the vet or even surgery.
I will never get a "toy" dog in my life again. In my opinion those breeders should be shut down, cruel to the animal, they have nothing but health problems.

Are the stools runny or hard? What color are they?

With her 'smelling', shaking and the constipation, I think you need to get her a check up. All of this is starting to add up to possible serious health problems.

The stools are hard.

You could try feeding her yogurt. A small dog would need a decent soup spoons worth.

Sometimes yogurt just helps things move along.. Kind of like what it does to us when we're feeling a bit constipated. Ive used it before.. Works pretty good.

Vegetable oil can also help.
It tends to loosen things up and lubricate.

It's good for their skin and coat too.

Just add a tablespoon or so to his food.