A sort of basic understanding of how to implement it would be to assume you have a points-based system for admission, which takes into account things like previous grades, standardized test scores, etc., and normally has a minimum threshold of n points for admission.
One way to think of affirmative action is that it says "people from this group, on average, will score k points lower not because of a lack of ability or intelligence, but because of a lack of opportunities earlier in life due to social inequalities", and then asks questions about whether a score that is within k points of n should be admitted.
The real implementations are more complicated, of course, but this is the basic idea. The main problem with it is that starting to apply remedies for inequality after someone has already lived through 18 years of it -- and 18 important, formative years at that -- is nowhere near enough.