Converting a varchar date into a date (dd/mm/yy)
I understand your problem to be how to successfully convert the string into a DATE value. An undelimited string of integers is assumed to be Year-Month-Day order.  (And, of course, I agree with the comments that dates should be stored in DATE data types in the database.)

Reviewing the MSDN CONVERT documentation does not show a built-in conversion for your string, but it is easy to work around.

http://msdn.microsoft.com/en-us/library/ms187928.aspx -- CAST and CONVERT  

I changed the month to 8 to make it easier to double check.  Using the CONVERT style option 3, you can do the following:

DECLARE @String VARCHAR(10);
DECLARE @DateValue DATE;
SET @String = '250809'; 

-- Convert your undelimited string DDMMYY into a DATE
-- First: Add / between the string parts.
SET @STRING = SUBSTRING(@String,1,2)+'/'+
     SUBSTRING(@String,3,2)+'/'+SUBSTRING(@String,5,2);
-- Second: Convert using STYLE 3 to get DD/MM/YY interpretation
SELECT @DateValue = CONVERT(Date, @String, 3);

-- Using the DATE 
-- Select the value in default Year-Month-Day
SELECT @DateValue AS DefaultFormat;    
-- Select the value formatted as dd/mm/yy
SELECT CONVERT(VARCHAR(20),@DateValue,3) AS [DD/MM/YY];


The results of the last two selects are:

DefaultFormat
-------------
2009-08-25

DD/MM/YY
--------
25/08/09


To get your DATE formatted in the way you want it, you have to insert the '/' delimiters then use the STYLE 3 in converting from the string to the DATE. (I am sure that there are other workarounds and conversion styles that would work as well.)

Likewise when displaying the DATE as you desire, you need to use STYLE 3