The approval process takes up to 6 months from the time IAC accepts your Registration of Interest to your being approved as suitable adopters.
How long you would wait for a match with a child will vary from country to country and on a case by case basis and for adoption from some countries you could wait for several years.
If you need to adopt in the UK after having completed the procedures in the overseas country, the child must have lived with you for 10 weeks (for adoptions from countries which are Convention countries), 6 months for adoption from non-Convention countries (or 12 months if the proper procedures have not been followed) before you can apply to the Court in the UK. An adoption order might not be made for a further 6-9 months.
Adopting a child from overseas is a long and complex process and it is important to understand that before you start on the journey.