Judaism was incredibly diverse in the first century. Judaea had been through two centuries of civil war and unrest over religion and politics, with more on the horizon. Their scriptural canon was still undefined, and there were numerous sects that we know of (and perhaps more we don't know of) with very different views.

The Pharisees were popular among the public and one of the two mains sects that vied for control of the priesthood. They adhered to both the Torah law and the prophets, and they had their own interpretations that differed from other groups. The believed in an afterlife (resurrection of the dead) and in a future messiah. This group survived the Roman wars and evolved into modern Rabbinic Judaism.

The Sadducees were more influential among the wealthy. They were associated with the priestly caste, they rejected all scriptures but the Torah, and they did not believe in an afterlife. They were generally opponents of the Pharisees in Judaean politics. They pretty much died out after 70 CE.

The Essenes were ascetics who rejected the temple establishment as corrupt. They kept strict purity and dietary laws, and some of them were celibate.

The Yahad were the group associated with the Dead Sea Scrolls. They may have been a sect of Essenes. They had a diverse body of scripture which included creative reinterpretation of older prophetic texts, and they had an apocalyptic worldview with the expectation of one or more coming messiahs.

The Zealots emerged in the mid-first century. Originally the term just meant "those who were zealous for God", but they eventually sought to incite the Jews to rebel against Rome.

The Therapeutae were a monastic sect found in the diaspora, particularly in Alexandria. Little is known about their specific beliefs and practices.

The Jewish Gnostics/Mystics had more radical views of theology. They saw the world in more spiritual terms, may have practiced magic, and believed that salvation was obtained through secret knowledge. Some groups venerated Enoch, Melchizedek, and other figures from Jewish myth as divine or semi-divine.

The Samaritans were the result of a religious and ethnic schism between the Israelites of Judaea and northern Palestine. Their main area of contention with other Jews was whether the temple should be located in Jerusalem or at Mt. Gerizim. The destruction of their temple in the second century BCE by the Judaeans decided the matter, but the Samaritan sect still survives today. Their scriptures consist of the Torah and their own version of Joshua.

We might also add the God-fearers: Greeks and other Gentiles who attended Jewish synagogues and were full or partial Jewish converts. This may be the movement that evolved into Christianity.

I'm not a historian and am not prepared to give a comprehensive answer but I can recommend an excellent book that gives in depth look - Professor Lawrence Schiffman's "From Text to Tradition". You can also check out his AMA on r/judaism from last month.

Judaism during that time period was very similar to Judaism today. The main difference is that the Temple still existed, so the sacrifices and other practices specifically associated with the Temple were still practiced. But religious practices in the life of the average Jew were basically the same as far as the rest of the 613 commandments are concerned.