There are various options here, all presuming you are running separate installations of Magento, you may want to refer to this information.
You can either have a central repository (MDM/PIM) and send the product information to the target instances as it is updated, use a point-to-point interface, or use an ETL solution. Obviously you can also have CSV imports and manual uploads however we presume that you would want the process automated.
You will need to use one of the Magento stores as the master repository then you can use point-to-point, this will be the quickest to implement but the most difficult to maintain. ETL applications are the solutions most companies use as a hub which takes the data and sends it to multiple targets due to the flexibility of using an intermediate solution.
You need to chose first if you will use a master Magento instance as the PIM or implement a PIM application. If using Magento as the PIM from there you can decide on coding a point-to-point interface or using an ETL solution.
We are just releasing a SaaS ETL service and have live a SaaS MDM (PIM), our parent can provide in-house MDM & ETL solutions should you need any more information.