It is known that Death the Kid is Lord Shinigami's son. However, how were both of them born ? And why does Lord Shinigami look like a Duskull while Kid and the Kishin are both humanoïds ?
In chapter 47 of the manga, it is mentioned that
A Shinigami is capable of reproduction, such beings possessing groins.
However, Shinigami are also capable of asexual reproduction, as explained in volume 9.
Shinigami can asexually reproduce by creating fragments of themselves and create a being. These beings, rather then be a replicate of the parent, can spawn off their own personality
Also, as for the humanoid part, it is implied by Death the Kid that his dad has a face. He says early on in the series that he "rarely takes off his mask." This is supported by the fact that Kid has his own Death mask and cloak that he wears on the way to retrieve Eibon's magic tool from the eternally-running train in the desert. When he wears them he looks just like Lord Death
It can be assumed that upon becoming a fully-fledged Lord of Death, a person foregoes his human form for the black, shadowy form Lord Death takes.