What is the ruling of Islam regarding a married woman committing adultery, as she was found with a strange man in her bedroom?

It is not permissible to accuse a Muslim of indecency without clear proof. A Muslim's indecency, if proven, should be concealed. One should strive to change evil (munkar) if able. As for the implementation of legal punishments (hudud), that is the prerogative of the ruler. In dealing with a disobedient sister, one should choose what is most beneficial for her reform, whether through shunning or through advice and persistent connection.