In the baptismal service those appropriate adults profess their own faith and promise to give the child a Christian upbringing.
In the case of adult baptism the person himself or herself makes the appropriate promises.
Baptism is normally administered at Sunday worship in front of the congregation. This emphasizes the nature of the sacrament as incorporation into the body of Christ and the life of the Church. There is a little more flexibility in the case of genuine emergencies, normally in a hospital situation.