Assuming that the column is of type 'date' - to update the column with a specific value you could say

update table_name set column_name = to_date('02/06/2001 13:24:04', 'mm/dd/yyyy hh24:mi:ss') where .....

To update with the sysdate, you could just say
update ..... set column_name = sysdate where .....


Hope this helps.