How do the Noble Families work in Bleach?
I do not think they went deeper into the noble houses, so I believe there is no current information available about "How to become a noble". All the currently available information on the 4 noble houses can be found here.

There they also state:


  The Noble Houses of Soul Society have an unclear role in the culture, social and governmental aspects of that dimensions existence.


Some speculation from my side: I think that they were either appointed by the Soul King or the Central 46. And I also believe the divisions are involved in this.


  There is reason to believe that the captaincy of the 6th Division runs in the Kuchiki family, as at least two members, both of them were family heads, have held the title captain and two other known members have been lieutenant and 3rd seat respectively. 


This part is just speculation though.