Having the incest trait, either by obtaining it with arcane essences or by having sex with relatives, will allow you to father/mother children with the incest trait. You can also enchant mystery kink with the incest trait and give it to your non-special character partner to increase the chances. Also, no one gives you that quest, per se, it pops up automatically when you reach a high enough relation ship with a generated npc.
After that, you just visit Lilaya and select the option "Accommodation" and you'll be given permission to modify rooms to become guest rooms, which will then allow you to offer rooms to wandering npc's that you have a high enough relationship with.
Oh, also, as an aside, you can give your offspring incest elixirs after you reach high enough affinity with them\.