Have you added the column while you are not in an editing session first? Adding columns cannot be done while editing. Also, if you are using SDE data, you have to have priveleges granted by the SDE administrator to alter the schema of an SDE table.
If you have added the column and not cannot modify the data in the table, let us know. What database are you using for the table, since editing may differ for some databases? Also, what version of ArcGIS are you using?