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.
In the audit track you will have access to course videos, lectures, readings, and ungraded practice assignments and can participate as much, or as little, as you like for the expected length of the course. In the audit track you will not have access to graded assignments, and no certificates are awarded when auditing.
You can see the expected length of the course on the course information page:
You are welcome to pay and upgrade to the verified certificate track later. After upgrading you would be able to see the graded assignments and work towards earning a certificate. You can see the deadline to upgrade on the course's Home tab.