Data Governance organizations vary according to company culture and maturity. Your operating model could include a council or steering committee; data governance working groups could be organized by business unit or focused around certain strategic initiatives. An essential step is to assign the appropriate organizational responsibility and corresponding ownership over data domains.
The success of Data Governance relies on clearly defined roles and responsibilities and the ability to monitor ownership and execution. Don't worry if you cannot obtain full responsibilities coverage from the start. It is normal to have varying degrees of maturity (e.g., maybe you managed to identify data stewards in Sales, but not yet in Finance).