To take a course for free, click "Enroll Now" on the course information page and then select "Audit This Course". This will allow you to join a course without paying for the verified certificate track.
You will have access to course videos, lectures, readings, etc., and can participate as much, or as little, as you like. There is no penalty for registering for an edX course and not completing the assignments or exams. No certificates are awarded when auditing.
You are welcome to pay and upgrade to the verified certificate track in the beginning of a course. Most courses allow upgrading within the first two weeks. You can see the exact deadline on the course's Home tab.