There are many ways to do this. I guess that is the reason you don't get response. Maybe you need to make it more specific.
If just use php and mysql
Make the remote database export to xml, text file, soap and then your central server gether them etc. merge them into your central database. Or your mysql dump the remote, ftp it etc. These tasks could be manually done or you can write cron to do these automatically. These are the ways that if you don't have direct tcp access to the remote mysql database.
If you have direct tcp access to remote database. then things will be very simple, you can just use php remote access these database and treate these database almost as they are running at the same server. very simple.
Or if your remote database doesn't allow tcp access but allow ssh access to the mysql for the security reason, then you can use ssh port forwarding, a little bit tricky then.