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.