I was wondering whether anyone might be able to tell me in layman's terms how to convert a polygon layer to a Grid file in ArcGIS 10.1 or ArcGIS 10.2?
You should use the Polygon to raster function (which requires Spatial analyst extension).
Don't worry about
Depending on how close you would want to look at your grid, you should set the
For this kind of conversion, you need to choose the attribute field that you want to store in the grid, because a grid can only have one thematic information. This is the value field that you need to define.
Knowing that, you can use one of the "Feature to Raster" tools for the conversion, or in your case maybe Polygon to raster which is more specific (but you then need the 3D or Spatial Analyst extension, or an advanced licence).
For an output in a GRID format, your output workspace must not be a geodatabase, and you must not write any file extension.