Teshuva, to my knowledge, would take place in a ritual bathing pool called a Mikveh. Mikveh's were typically constructed with a set of steps separated by a middle divider (a risen stone divider several inches to a foot high) next to the entrance of the outer court of a Jewish synagogue or temple or in a town square. This water was also heated or "living" water, as the Jews called it, typically provided by hot springs or other means. Jews, before entering the Mikveh, often fasted several days to cleanse soul, spirit, and body, as the Mikveh was a required ritual bath upon intention to enter a synagogue or temple, as well as a pool used for other religious purification. Separate Mikveh's existed for men and for women. The partaker of the Teshuva would then walk down one side of the steps unclean, immerse oneself in water, and then walk up and out of the pool on the other side of the steps and be proclaimed clean. Only then were they allowed to enter the temple. The pools of Bathesda, and in particular, the pool of Siloam were probably both Mikvehs to this effect. (Bathesda in the gospel mentioning the "stirring of the waters" provided by it's probable hot springs periodically).
Partaking in a Christian baptism was essentially based on the same premise as the Teshuva. Baptism in ancient Judaism had both to do with ritual cleanness, but also to do with agreement. In obtaining water baptism you agreed to the laws, statutes, and beliefs of the institute or theology presented by the temple or prophet providing the means of baptism. In effect, it is symbolic of dying to your old way of thinking, and being reborn in unity with the beliefs of your baptizer. John the Baptist, for example, was readying hearts for Christ's arrival by preaching repentance, or the realization of one being a sinner needing forgiveness. One cannot fix a problem if one is in denial of it existing, after all. Then, upon Christ showing up, Jesus provided the answer to this revelation of sin in man. Water baptisms, to this effect, helped others in the Christian church publicly identify with John the Baptist's idea of needed repentance, that those who got baptized, were publicly proclaiming their agreement with their baptizers that Christ was the one who would solve their issues of sin.