The rise of Christianity in Rome came about by several factors. First of all, communication and trade throughout all of Europe became faster due to the Romans conquering and stabilizing much of the Mediterranean. Around 50 AD Saint Paul of Tarsus began conducting extensive missionary work, spreading the word of Christiniaity throughout the Roman Empire. The religion also carried appeal to the masses, especially the lower class and slaves because of its focus on caring for the sick. It gave many downtrodden within the empire new hope.
Christiniaty became dominant in the Roman Empire when Emperor Constantine coverted to Christianity and moved the capital to Constaninople, surrounded by Christian faithful. Every successive emporor (save for one) was henceforth Christian, and over the next few decades Pagan houses of worship were destroyed and Paganism eventually outlawed.