Set up a meeting with the registrar of your college or university. The school can provide you with a list of classes that your college allows you to test out of through the school. Also, ask your registrar to give you a list of what classes you can earn credit for with your SAT scores, ACT scores, Advanced Placement (AP) exams, International Baccalaureate (IB) exams and College Level Examination Program Scores (CLEP).
Contact the head of the department for any course that you wish to test out of and ask what kind of material is on the test. Set up an appointment to take that test and study the material that will be on it before you go to take it.
Sign up for AP, CLEP and IB Exams through the College Board. A variety of exams are available in every discipline, and you can test out of as many as two classes for each perfect score you get on the test. Slightly lower scores may allow you to test out of one class. Anything below average will not exempt you from taking the same class in college. Once you've taken the test, have the scores reported to your registrar, and they should reflect the courses you've exempted from as complete on your transcript.
Show you ACT and SAT scores to the registrar and request exemptions from low-level math and science classes if you're in the 95th percentile or above in any given category. Not all schools offer this method of exemption, though, so be sure that you are eligible before you insist on it.
Replace a class that you wish to test out of with a similar course you've taken at another college. Write up a document explaining why the course should replace the course you're attempting to be exempt from, and discuss it with the head of the department that manages that course. If they'll sign off on it, the registrar may be willing to accept the exemption.