How do I put professional affiliations on a CV?

By 'Professional Affiliations' it is meant that one is a member of certain professional association such as IEEE, ACM, ICE, ASCE etc.

These professional bodies often arranges conferences which anyone can attend, so registering for the conferences does not mean that one is a member of a organizing body. Conference participation information may be put into your publication list as conference papers and/or given talks section.

So, You should only list the organisations as professional affiliations of which you are a member.

Any professional association in which you have been a member.

Conferences are not included in that category, unless they imply membership in some association. For example, registering for the biannual meeting of the Materials Research Society includes membership fees, so if you participated in a meeting, you were a member.

Regarding past membership, I would only include it if you were a member for a significant time.

Rashed's answer is correct. In addition, though, it is not uncommon to place other notable affiliations towards the end of the resume, if there is space, under whatever title is appropriate. For example, in my resume, I have a "Community Service" section, where I list my membership on various nonprofit boards of directors. If you hold officer position in any other notable groups you could list them similarly.