This depends on the company's articles. Often new directors may be appointed by the board. Alternatively they may be appointed at a shareholders' (general) meeting.
If directors are appointed at a shareholders' meeting, they must be nominated either by the board of directors or by a shareholder. Shareholders who wish to nominate a director must give notice of their intention to make the nomination, within strict time limits.
The directors may refuse to call a shareholders' general meeting to consider a shareholder's nomination. However, shareholders with at least 5 per cent of the voting rights (or, sometimes, 10 per cent) can require that a general meeting be held.
Alternatively, more specific rights to choose directors may be included in the articles of association.
A majority of the shareholders can always vote to remove a director from office, (though, if he has a service agreement, the director may be entitled to damages for wrongful or unfair dismissal). Shareholders must follow a special procedure so legal advice is strongly advised.