How did hinduism, buddhism, and islam become established in south east asia?

Link trades between India and the South East Asia has been around even before the modern times. This led to the establishment of Hinduism in the region.
Buddhism arrived in South East Asia through China. Buddhist missionaries reached China leading to a strong establishment of the religion/philosophy in the country.
Islam arrived in South East Asia also from Indian trades but it become established with the efforts of Sufi's who incorporated Islam with the local traditions and beliefs.