WARN: it seems the 'Join Attributes' function ha been removed from fTools 0.6.2, solution for me was to downgrade to 0.6.1.
You can use QGIS to perform the operation you want, please proceed as follows:
- if not installed already, install Quantum GIS (an Open Source desktop GIS) and then install fTools as described here
- export the mdb table or query into dbf format (from Access, select the object, right click, export)
- open the region shapefile in qgis
- click on the Vector menu, Data management, Join attributes (I am translating roughly from my localized version)
- fill out the dialog and then click ok
- you should now have another layer with data from btoh the region shapefile and the dbf file
See the image below for an example: