I need to define the boundary of a number of towns. I have found maps of some of the towns in google maps but have no idea how I can digitize or export them for use in ArcMap. So far i have not seen any tools in Google Maps that could be used.
In addition to @Matt's answer, which is relatively easier, you can use Google's My Maps. Assuming you have a Google account, creating a map is explained here and by using draw a line tool, you can create polygons. Even though it says line, the sub menu says Add line or shape and closing your line will create a polygon.
Once you finish your map, in the map options, you will find Export to KML. Then you can convert KML to ArcGIS vector formats by using KML to Layer tool.
Try Google Earth instead. Essentially the same as Maps, but you can draw shapes and export them as .kml files.