1)    When a person hears a blessing, whether it is a blessing which he is listening to in order to fulfil an obligation or whether it is a normal blessing, he must respond with “Amen”. He should teach his children also to respond with “Amen”, for as soon as a child answers Amen he has a portion in the world to come. (Shulchan Aruch and Mishne Berurah 124)

2)    The correct intention to have when responding Amen is as follows: If he is responding to a blessing of either praise or thanksgiving (e.g. melech mehullal batishbachos etc.), he should intend when saying Amen that it means “The blessing is true and I believe in it”. If it is a request (e.g. Chonen Hada’as), he should intend as well as the fact that the blessing is true that “May it be Your will that You should also favor us with knowledge!”. (ibid)