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Companies Act does not deal with appointment of Chairman of a company.  It only talks about Chairman of a meeting (Sec.175) or Chairman of the Board (Sec.217).  It is only in practice that many companies appoint one of its directors as regular Chairman of the company who becomes chairman of the Board and general meetings.  If regular Chairman is not present, members can appoint someone else as chairman of the meeting.  He does not get any additional powers or duties as such except as provided in the Act with reference to meetings. Chairman can be appointed by passing Board resolution.

Thanks

Agreed with Agarwal ji.

If you are talking about the Chairman of the Board then the provisions of the Companies Act govern otherwise it is the matter of company's management to designate anyone as Chairman, President, Vice President.