The way to apply for exemption differs among universities.
In the UK, deferment is requested via the UCAS application form. One has to indicate the preferred year of entry for every course applied on the form.
In Australia, the preference is also indicated on the application form, but often student will also be asked to provide complete course details of the the modules previously studied (including course sypnosis, aims, contact hours, textbooks used etc). Students may also be requested to assist the university with module matching by completing a credit exemption request form. In the case where the university has a credit arrangement in place with your school, exemption may be considered automatically and included in your offer.
Universities in the US do not typically assess exemptions until one has received the offer, and in many cases after one has also accepted the offer.
At theRightU, we work with a number of US universities that are able to provide you with an indication of the number of credits exempted when you receive your offer.