Hi Dylan
Welcome to the forum!!
The process for sending a request to someone overseas is very similar to sending a request to someone within your country.
You will need the following:
1. A letter addressed to the celebrity you're writing to
2. Something for the celebrity to sign - e.g. photo (optional)
3. A self addressed envelope (addressed to you, make sure it will fit your photo if you're sending one - or big enough to fit the size of the photo you're anticipating) and enough International Reply Coupons (IRC) to return your envelope (if you have enough UK stamps you can stick them on the envelope instead of sending IRC's).
4. Another envelope addressed to the celebrity. This envelope will include your letter, self addressed envelope etc. Stick enough stamps on the envelope to send it off to London.
Information on IRC's can be found
here. Put simply, these coupons are exchanged by the celebrity for stamps to stick on your SAE to send back to you. One IRC will cover a standard letter back to you. Larger envelopes (such as 9x12 inch) will require 2 or 3.
If you would like information on postage costs, please take a look
here.
I hope this helps. If you have any more questions, please feel to ask!
nowandagain [rockon]