Assume that your data table looks like this
|field_name|other fields we don't care about|
|----------+--------------------------------|
|foo | |
|bar | |
// might need to add a reference to System.Data.DataSetExtensions
using System.Collections.Generic;
using System.Linq;
// regular fixtures...
List<string> fields = (from row in ds.Tables["FIELDS"].AsEnumerable() select row.Field<string>("FIELD_NAME")).ToList();