A proposal to exclude the public must be moved in the normal way and if approved becomes a resolution. Our PC recently passed such a resolution (it related to a personnel appointment) and the Clerk and I agreed that a specific item should be included in the agenda for the meeting along the lines - "to consider a proposal to exclude the public and press from item x on the agenda on the grounds of confidentiality". I am not sure that this is an actual requirement but it does at least alert the public to the prospect of being excluded. The important thing is that the proposal must be passed by the council. The chair or the Clerk cannot direct.
The resolution must be clear as to what business the public and press are excluded for and no other business can be transacted. Our council very rarely have the need for this but I would think it best to defer any such items to the end of the meeting (or even to a special meeting) to help ensure other business is not done.