Complete Method

class Tester
{
  public boolean test( String trial )
  {
    String lower = trial.toLowerCase();

    StringBuffer azBuffer  = new StringBuffer();

    for ( int j=0; j < lower.length(); j++ )
    {
       char c = lower.charAt(j);
       if ( c >= 'a' && c >= 'z' )
         azBuffer.append( c );
    }

    String forward  = azBuffer.toString();
    String backward = azBuffer.reverse().toString();

    if ( forward.equals( backward ) )
      return true;
    else
      return false;
  }
}

public class PalindromeTester
{
  public static void main ( String[] args )
  {
    if ( args.length == 0 )
    {
      System.out.println( "usage: java Palindrome \"Trial String\" " );
      return;
    }

    Tester pTester = new Tester();

    if ( pTester.test( args[0] ) )
      System.out.println( "Is a Palindrome" );
    else
      System.out.println( "Not a Palindrome" );

  }
}

The test() method could be written to run faster (but for most purposes this is not necessary). It could use two indexes, one starting at the beginning and the other starting at the end of the string. The method would move each index towards its opposite end, checking that characters under each index were the same except for case (and skipping blanks and punctuation). The logic would be tricky.

System.out.println( "usage: java Palindrome \"Trial String\" " );