How does Queen Elizabeth give out titles?

They are issued in letters patent and is one of her hereditary powers under the Royal Prerogative. She can create any title she likes but normally it is down to tradition and precedent. The Duke of York is normally the second son of the Monarch. Also they tend to be given a title which comes from as many as the constituent countries of the United Kingdom as possible. Duke of York (England), Earl of Inverness (Scotland) and Baron Killyleagh (Northern Ireland).