A doll is a special trinket depicting one of the Ocean Masters or Ringers. Twenty-eight OMs and eleven of the Ringers have dolls. (There is no Eris doll.)
They are given out by the OM or Ringer who is depicted. They do not give out dolls on demand.
For details on how to earn one in an event, please see the events page. For dolls where there is no contest nor guidelines for winning one, the OM must feel that you deserve one to be awarded it. There is no other way to obtain dolls, apart from buying them off other players.