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You seem like your on the right track.  I would caution that you don't need to know everything about every aspect of the organization to accomplish the goals of the project.  It sounds like you primarily will need to focus on data and reports.  Of course, if the organization is small having some knowledge of the organizations goals and purpose and an understanding of the roles of each department won't hurt.

But to come back to your main focus, consolidating multiple databaes, here are a few pointers:

1. Always start with requirements.  In this case, your requirements will be the reports that the company needs to generate.  Talk to the various groups who run reports against the data.  This may be as simple as manipluation of data in spreadsheets.  Or they may geneerate reports directly from the database using some software like Business Objects.  Either way, your first step is to identify all existing reports.
2. Next identfiy new requirements.  Their current system is obviously falling short.   They said that they currently have sub-optimal customer relationship management. So you should sit with the various people who need to generate reports and find out what new reports they feel they could use.
3. Next you will want to analyze the current state of the existing databases and data.  An ERD diagram for each may make sense. 
4. Once you have modeled the AS-IS state of there disparate databases, you will need to model the TO-BE or future state of the consolidated data base.  While doing this consider the new data that you want to add to support new reporting.   
5. Once the TO-BE state is modeled you will have to develop a plan for migrating data from each of the old databases to the new database.  Consider what you will do if you have repeated data across existing databases that conflicts. 

Hopefully, this will help  get you started.  I tried to keep it high level here.  I'm sure you will have other questions as you dig in.