First, get your pets romantic enough to have babies. When there very interested in each other, buy a dog house (or any pet house) select the house. There SHOULD be an interaction that says try for puppieskittens. Click it. Just like sim humans, a little door will shut to give them privacy, and you'll here that music that usually plays when their woohooing. You should hear the ring that plays when the female is pregnant. Soon you'll have the babies!! Hope this helped!
Your human Sim must first be good friends with another Sim of the opposite gender. Use social interactions listed under the "Romantic.." sub-menu until the other Sim starts to find you irresistable. Usually, simply "Kiss" repeatedly will do the trick. Once irresistable, you may choose the "Try for Baby" social interaction, also listed under "Romantic.."
The Sims will automatically walk to a double-bed (keep in mind this will not work if you only have single-beds available) and do their business. Certain problems, such as other Sims in the room, low stat bars, or no room in the household can prevent pregnancy. Listen for the happy-bells sound effect, which signifies pregnancy in both Sims and pets. Keep repeating the "Try for Baby" interaction until you hear the bells.
After about 12 hours or so, your Sim will automatically pull you out of the game for a quick change of clothes. That belly gets big and your choices are limited. Thankfully, it's only for a couple of days, so just be patient!
The Sim will be pregnant for about 2 1/2 days before going into labor. Use this time wisely! Take them out to eat at the restaurant, get a massage, and whatever you do, keep those stat bars high!
When the Sim goes into labor, you do not have to go to the hospital, you may choose to stay home for a good old-fashioned home birth, but going to the hospital will give your Sim the benefit of returning home with the other parent in tow to help with the new baby(s) if they don't live in your Sim's house with them.
Now, just keep the baby(s) happy to keep to Social Services worker from taking them away due to your attrocious parenting skills! ;)
So first you must become good friends/best friends with someone in town. Then under the friendly category when talking to them, ask them to move in BUT, instead of THEM moving in, make your pet live with them. So on the left side is your house. On the right side is theirs. Move the pets you don't want from the left to right side (along with the person you were talking to and asked to move in.)