I downloaded a race called "The Ashen - Oriental Beauty Race" and another mod called "Beautiful Characters and Companions". I wanted to change one of the companions to the Ashen race. But I do not know how to change NPC to a custom race in Skyrim CK. What I did was, I choose the character that I wanted to change and then I changed her race from Breton to Ashen. But that did not work. When I went in-game to see her, she was a animal instead of the Ashen race. Please how to do I change a NPC (companion) to a custom race? Is there any kind of tutorial?

Make sure you set the morphrace under race to a template of the race you want. There is a glitch if you do not set these that causes the created race to display incorrectly.

Okay thanks I will do that. Is there anymore steps to changing a NPC to a custom race? Or is that just it?

The reason it didn't work was because of mod isolation. The rough explanation is that an esp cannot use any resources from other esp or esm files unless the other file is set as a master of itself. The CK will automatically set any loaded esm files as master to the current file.

For example, I load A.esm, B.esm, C.esp in the CK. I change some stuff, and then save the mod as D.esp. The master files for D.esp would be A.esm and B.esm. If I used anything from C.esp in D.esp, then those would be invalid references, which would result in errors when trying to play with D.esp.

http://www.truancyfactory.com/tutorials/oblivion/oblivion01.html explains it better. It's written for Oblivion, but the principle is still the same.