Ask your teachers for help. Teachers have gone through the same process you're about to undertake, and likely they remember how it felt to prepare for the college placement exams. Sit down with your math teacher and work on the sections you have had trouble with, or ask your social studies teacher to quiz you on the most important events of the 19th century. Whichever placement test you have to take, extra help from your teachers will propel you toward more advanced classes in college, which will save you time in the long run, as you might test out of certain required classes.
Visit your school's website. Search through the different departments for the curriculum guides of the subjects you're looking to test out of. Find different teachers' syllabuses and determine if you already know all there is to know about a particular topic, or if you know nothing about it and will need to do some research. Cross-referencing will help you determine where your strengths and weaknesses are.
Review the college board tests you took to gain entrance into college. Take more ACT and SAT practice tests. While these may not cover exactly what your new school is looking for, they will help you keep your frame of mind at a college level of study.
Review your class notes and make up your own tests. Create multiple choice or fill-in-the-blank tests to review the next week, once the information isn't as fresh in your head.