The first business of the council's annual meeting is to elect a chairperson. The annual meeting is held in May each year. It is up to the council to decide how to go about this, although an obvious requirement is that people who are proposed must be willing to take up the office. The person appointed has to be present at the meeting because they must sign the acceptance of office at the meeting. Candidates can put themselves forward, or councillors can request them to be considered. The final decision must be a vote in the council to appoint a particular person.
A parish council may choose to be a town council if that seems appropriate. This does not alter the rules governing the council at all. The chairperson of a town council has the honorary title of mayor. The vice-chair of a town council is likewise the deputy mayor.
CORRECTION: I was mistaken in thinking the candidate for chairman must be present. The person elected must sign a declaration of acceptance prior to officiating. That means that if they are present, the declaration must be signed immediately, at the meeting. However, there is no statutory bar to electing a council member who is not present. They must still sign a declaration before attending a meeting as chairman.