Now onto your PC. Download the MySQL ODBC plugin (MUST be version 3.51 and MUST be 32 bit: http://dev.mysql.com/downloads/connector/odbc/3.51.html ).
Install it on your PC (I would suggest using a 32 bit machine to save a lot of messing around).
Go to Windows Control Panel > Administrative Tools > Data Sources and click the tab for System DSN (very important - won't work unless it's System DSN) and click Add.
You'll see the MYSQL ODBC connector you installed listed.
Now add the following: Domain, DB name, DB user name, DB password.
Test the connection.
Now in Filemaker Pro select File > Sharing and switch on the ODBC/JDBC radio button and select for all (or limited) users.
Next File > Manage External Sources > New > and enter a name for the connection.
Click the ODBC radio button and specify the data source (this should pull up your MySQL ODBC connection. If it doesn't something's amiss). Add in the authentication details (User Name and Password). Click OK.
You now have a live connection between MySQL and Filemaker.
Next stage is adding fields.
Again in Filemaker:
File > Manage > Database > Relationships
You'll see any existing table(s) and the fields it contains there. Click the 'Add Table' button and from the Data Source drop down select your MySQL connection. You'll see all of the Joomla tables displayed. Now select the appropriate table (in my case I was connecting Virtuemart so used the 'jos_vm_product' table and the 'jos_vm_product_price').
You'll see your new table displayed with all its fields.
Next step is to make the relationships. Again using my Virtuemart example I made a new field in my existing database table (you can do this from the View > Layout Mode (although sure there's a better way - I'm a complete Filemaker novice) for Product ID.
Connect up the matching fields (these need to be unique so for example an email field, etc) between the Filemaker table and the Joomla table and click OK.
Now go into View > Layout and you can add in Joomla fields to your Filemaker layout. Simply add a new field and select the Joomla table and the field you want.
Now when you update either Filemaker or Joomla the data will synch in real time.
Best of luck and of course if you'd rather we did this for you just contact us.