The first things that you will need are as follows :For an Adopted person...
Birth name
Birth date
Birth place
Mothers name
Fathers name
All of which can be found on their birth certificate, which can be obtained through the local office which dealt with the oringinal registration, or from the family records office. (see useful addresses)
Ideally you need a rough date of adoption, place of adoption, which court dealt with the adoption and at what age the adoptee was adopted.
You can place yourself on the adoption contact register which cost approx' 30 GBP.
this only works if the adoptee is also on the register and looking for thier birth family.
If you know which authority dealt with the adoption, you are allowed to contact them and ask weather or not the adoptee has read thier file, this is the only imformation that they are allowed to tell you.
If the adoptee has read thier file all it comfirms is that they know they are adopted (less of a shock should you just turn up)
Place messages on EVERY message board you can find (some of which are listed under links).but please remember the person you are looking for, may not know they are adopted and may not even in some cases want to be found.
Accept help from anyone who offers it, even if they are only going over ground that you have already covered. they might just give you that little piece of imformation you need.