How do you make the dogs on The Sims Unleashed to have litter?

If you mean litter as in litter box then you can't. But if you mean litter as in puppies, you need to get two dogs, one male and one female, that are the same breed. After awhile, a box will pop up asking you if you want to breed your pets.

Well you have to have a male and a female dog. Then you have you have to wait, while the dogs get to know each other.

Then when the dogs know each other enough a notice will pop up and say would you like to breed your pets say yes.

Then a box will appear and a puppy will be in it but you can not see him/her.

Then it will get older and another notice will pop up asking if you would like to keep or sell your pet. That is how you do it.

You need a male and female dog. They DO NOT have to be the same breed--you can breed a Dalmatian and an Alsatian and they will have a dog that is the same breed as either the mum or dad eg

Yellow Dog had puppy with Dalmatian
Puppy will be a yellow dog or a dalmatian.
A trick is to quickly pause and then save just before the pet grows up (it remains a baby for three days) and then if it's personality is rubbish you can change it.