Baptist is is a broad label which encompasses many divergent groups, so providing anything more than generalizations is difficult. This is complicated by the fact that one of the distinctives of Baptist doctrine is the independence of the local church. As such, these kinds of things are generally up to the discretion of each local congregation. Despite all that, however, some generalizations can be made which will largely hold true in most Baptist churches.
Baptists are opposed to rituals and repetition. They avoid reciting written prayers and following liturgies. For them, religion is a personal relationship between each individual Christian and God. As such, repetition of religious rituals or prayers are considered to be too static and non-individualistic. There is also a strong sense of the fallibility of mankind. As such, rote memorization and recitation of anything other than scripture would be generally frowned upon.
That is not to say that Baptist churches do not have official defined doctrines. Each local church has their own official doctrines which are agreed upon by all of the members of that church. These written doctrinal standards will vary from congregation to congregation, even within the same Baptist association. Typically, prospective members must agree to the entire set of stated doctrines before they are allowed to join the church.
Remember, in a Baptist church, only baptized Christians may join the church. Since Baptists believe in believer's baptism (as opposed to infant baptism), only those who are old enough to be baptized are allowed to join the church. As with everyone else, those being baptized must agree with the doctrines of the church before they can become members.
As far as formal training goes, there is none--at least not in the sense of a formal catechism. Children are typically educated in the doctrines of the church in Sunday School classes. It is also common to have separate services catering to children which occur during the same time as the main service for adults. It is also common for churches to require prospective members (and those seeking baptism) to attend a membership course in which the history, associations, and official doctrines of the church are covered in detail.