how do i make my sim give birth?

Your sim has a moodlet with a pacifier icon during pregnancy which will tell you which trimester your sim is in. Once in the 3rd trimester they will go into labour about 5 hours (minutes) after. In labour it will take 3 hours (minutes) for the baby to be born.

I believe there may be a cheat that speeds up pregnancy, however each time I've attempted to find/use one it does not work. But yes, you have to wait until they are in the third trimester and get a notification telling you that they have gone into labour.