You cannot have children in the conventional way in Skyrim whatsoever. However, you do have the ability to adopt certain children which you may come across during your travels. To do this your character will need a home and have completed the quest' innocence lost'. After this quest is when most people are greeted with the option to adopt as the quest ends with you murdering the witch-like proprietor of Riften and Skyrim's only orphanage. There are also further opportunities to adopt provided by the Hearthfire DLC.