How to automate assigning a "permit" number to multiple parcels with one owner?

[ScottTompkins]

I have a shapefile in which I would like to assign one permit number to cover one owner including all of his/her parcels...I would like to be able to calculate this in field calculator if possible? Essentially, I want to be able to assign all parcels owned by this individual the same number value. I realize I can do this manually and have been doing it that way already, but I simply don't have the expertise to automate this task.

[BarbaraSieg]

You'll need a table with the following two fields in it:
1. OwnerID from some field in the parcel shapefile attribute table that has the same value for all occurrences of that owner.
2. Permit number, as a numeric or string field, whatever suits your purposes.
Is there such an OwnerID in the parcel shapefile attribute table? If not, you'll need to add a field and populate it with a value unique to each owner, otherwise there's no way to automate the task. It could be the owner name, for instance, or some other ID value. Owner name may not be spelled exactly the same for every occurrence of that owner, so it may not be a good field to use. If there is no suitable field, you'll have to create one.

In this as in most map automation tasks, the major effort is in preparing the data. Once the necessary data exists, the operations on the data are generally straightforward.

If you have such a separate table (with OwnerID and Permit number) external to the shapefile, fine. If you don't have such a table, you can create one from the parcel attribute table: In a map, open the parcel attribute table and export the table from the table options menu as a new stand-alone table to DBF or geodatabase format.
In the exported stand-alone table, you can delete all the fields except the OwnerID, or you can leave some fields if desired.
There are probably multiple records for some owners. In ArcView 10, use the Delete Identical tool on the exported table:
  http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#/Delete_Identical/001700000053000000/
This removes all but one record for each unique OwnerID.
Then add a field for the Permit number and populate it manually. Now you have a table with one record for each unique Owner ID.

The next step is to Join the stand-alone table ("Tbl") to the shapefile on the OwnerID field: that is, in ArcMap, right-click the parcel layer > Joins & Relates > Join > Join attributes from a table.
In the Join wizard, the field in the layer is the OwnerID, the table to join to this layer is Tbl, and the field in Tbl to base the join on is the OwnerID field in that table.
Set the option to keep all records.
If you are running 10.0, validate the join. In any version, allow the tool to create an index on the join field, if asked.

View the joined layer attribute table. At the right side of the table you'll see the fields from Tbl.
A join is in effect within the map but does not permanently alter the shapefile attribute table. If you want to save those fields in the shapefile attribute table, do one of two things:
1. Right-click the joined layer > Data > Export Data, and export the joined layer to a new shapefile or feature class in a geodatabase.
Or:
2. Add a field (same data type as the Permit field) to the parcel layer attribute table. Use Field Calculator to copy the values from the joined Permit field into the new field, then remove the join.