I am a Brazilian citizen and my wife has dual nationality: Brazilian and British. Our son was born in Brazil. Now we are moving to the UK to stay for an indeterminate period of time. Does my son have the right to the UK citizenship? What are the requirements?
If your wife had British citizenship when the child was born, and she got her British citizenship "otherwise than by descent", then your son will automatically be a British citizen at birth, without doing anything.
Note that she had to have British "citizenship", not just British "nationality"; there are many kinds of British nationals, including British Overseas Territories citizens, British Overseas citizens, British Overseas citizen, etc. She needs to specifically be a "British citizen". "Otherwise than by descent" means that she was not herself born abroad and got British citizenship automatically through her parents; if she was born in Britain or she was naturalized in Britain, then she is a British citizen "otherwise than by descent".
See British Nationality Act of 1981, section 2 for more information.