I believe causes for canonization can only be started in the diocese by the Bishop which the person is from or spent a significant amount of time, in the case of religious the request comes their community superiors. I think the next step is that when submitting this information to Rome they need to provide evidence of the person’s heroic virtue. This requires them to do some research and, if the person is recently deceased, interview people that knew him or her. This step isn’t nearly as exhaustive as the canonization process moves forward when all their writings and public utterances are examined for doctrinal conformity and people are interviewed much more extensively and people that had contact with the person are asked to write in (this step can take years to complete).
Rome does not fund any of this so you’ll often see societys or groups formed to raise money to help pay for this. It’s at this stage that some causes can get weighted down as money drys up or people can only devote so much time to this or the other thing. Well-funded groups can hire professional researchers and historians and experts while causes for less notable people languish because the diocese can’t help with much or it’s a group of volunteers doing their best.
ChadS
