Go to the college bookstore and review the current edition. Many textbook authors will clearly spell out the differences between the current edition and the previous edition in the preface of the book. If the author's approach to teaching some of the materials has changed or different exercises are used, it is best to purchase the most recent edition.
Contact the professor. The newer edition of the textbook might simply have an added section that the professor does not plan to use or the chapters might be ordered differently but contain the same material. The professor will know the difference between the editions and will be able to tell you if the changes are too drastic for you to be able to use the older edition.
Compare textbook editions at the college's library. If the current edition does not list the changes and you are unable to reach the professor to ask about the differences, try the school library. Most colleges keep current and previous textbooks in the reference section for in-library use. With two editions side-by-side, you can compare indices, chapter summaries and exercises to determine whether or not it is feasible to use an older edition.