CSG membership is capped and new members are therefore considered only as openings arise. When openings do arise, invitations are extended to institutions whose reputations for excellence or innovation have come to the attention of the CSG. It is thus not necessary for prospective members to "apply," either formally or informally.
Nonetheless, if you do feel motivated to bring your institution to our attention, start by reviewing the current membership list. Find a CSG member whose CIO you know well and discuss your interest in joining. If that conversation fails to change your mind, ask your contact to pass along your interest to the membership committee. (He or she may well claim not to be aware there's a membership committee. That's not your problem.) It will help your case if you provide your contact with a short memo indicating: