You also have to be married to a Sim that lives in your household, that you can control. If you marry someone outside of your household they do move in, but without an additional character slot you cannot control them and when you attempt to have a baby, you will get an error message saying you need to find a compatible partner. Once you have reached level 10 relationship and got married, you’re almost there.
You need to progress through the game until about Player Level 10. This unlocks a new option in the Shopping Menu – babies. Once you have unlocked that category you need to purchase a Bassinet, or a crib. Place it somewhere in your house, preferably not in a cupboard under the stairs as that leads to anguish later in life – not magical powers and a stupid scar.
Once the Bassinet is placed in your house simply interact with it and choose whether to adopt a boy, adopt a girl or have your very own Sim baby.
You must first be married to another Sim as currently you are not able to adopt or have a baby without first being married.