Today the Catholic Church makes potential converts participate in the RCIA program. Before Vatican II could someone go into a Church and tell the priest he wants to be Catholic and receive baptism on the spot? If so, could this still be done?
This is not clear purely from Church law, but it appears unlikely. Canon 752, section 1 of the 1917 Code of Canon Law reads:
Adultus, nisi sciens et volens probeque instructus, ne baptizetur; insuper admonendus ut de peccatis suis doleat.
An adult is not to be baptized, unless knowing and willing, and having been properly instructed; moreover he is to be admonished so that he is sorry for his sins.
This is very nearly the same wording as in the current Code of Canon Law:
For an adult to be baptized, the person must have manifested the intention to receive baptism, have been instructed sufficiently about the truths of the faith and Christian obligations, and have been tested in the Christian life through the catechumenate. The adult is also to be urged to have sorrow for personal sins.
(Code of Canon Law , Canon 865, section 1)
Current canon law thus requires the catechumenate (participation in the Rite of Christian Initiation of Adults). But the Rite itself was not promulgated until 1972; thus, until that time it would be up to the bishop to decide what exactly constituted "proper instruction".