The data is already in a DataTable so you can iterate over that just as easily as you can an array.
VB Code:
For Each row As DataRow In myDataTable
MessageBox.Show(row("ZipCode").ToString())
Next row
You can get whatever field values you need from the row inside the loop and do whatever you need to do with them. Note that a DataSet is a container for DataTables and the DataRelations between them. You can access the individual DataTables through the Tables property. If you are only using a single DataTable then having a DataSet is pointless. If that's the case you should forget about the DataSet altogether and just work with a DataTable. You can pass a DataTable to the Fill method of a DataAdapter just as you would pass a DataSet.