Cynthia, In order to schedule a class, it must implement the Schedulable interface.  In this case, this should also be a batch class (that implements the Batchable interface) so that it can process an arbitrarily large number of Account records if necessary (up to 50 million).  Here's my version:

<pre>
public class update_tss_fields implements Schedulable, Database.Batchable<Account>
{
    // The Schedulable interface allows you to schedule the class and
    // makes it available in the scheduler UI.  To implement the interface,
    // you need the following method:

    public void execute( SchedulableContext context )
    {
        // all it will do is execute the batch process
        Database.executeBatch( this );
    }

    // The Batchable interface lets you process large numbers of records
    // in multiple small batches.  To implement the interface, you need
    // the following three methods:

    public Database.QueryLocator start( Database.BatchableContext context )
    {
        return Database.getQueryLocator
        (   'SELECT Id, TSS_Designation__c, TSS_Temporary_End_Date__c '
        +   'FROM Account '
        +   'WHERE TSS_Temporary_End_Date__c = TODAY'
        );
    }

    public void execute( Database.BatchableContext context, List<Account> accounts )
    {
        for ( Account account : accounts )
        {
            account.TSS_Designation__c = null;
            account.TSS_Temporary_End_Date__c = null;
        }
        update accounts;
    }

    public void finish( Database.BatchableContext context )
    {
        // nothing to do here...
    }
}
</pre>

BTW: Shruti was spot-on with her advice #1 & #4.  #2 isn't entirely true - you must query fields that you will write, as well as the ones you will read.  #3 is a common misconception - doing DML on an empty list does not cause an error and it does not count against DML limits - it just does nothing.  Let me know if you have any compilation problems.  I didn't actually compile this and there might be typos.