First of all, you should get information that your favourite celebrity has a fan based website or not. Almost all famous celebrities have their websites where their fans remain updated with the activities of these celebrities. Many fans send emails on these websites and also get response.
You should also try to find sources that could help you to get the postal address of the famous celebrity. You can also consult the directory which will help you in finding the current addresses of celebrities.
You should compile an email or a letter addressing to the celebrity and make sure you write it in a way that shows your respect to him or her.
Make sure you have written a letter or email in a compact way. Do not include unnecessary details which will create a bad impact.
Do not forget to add your email address in the letter which will help the celebrity to send his or her response after reading your letter.
Be patient while waiting for the response because sometimes it takes many days or even weeks to get response from a famous celebrity because of his or her busy schedule.