After being marched into exile in Babylonia, the Judaeans (we can call them Jews now) were deprived of the Holy Temple and their King. But unlike the people of the Kingdom of Israel, the Jews in Babylon did not become Lost. What they did was two things. They resumed local sacrificing like they had before the Holy Temple was built, and they began to write the Talmud.
The Talmud was created by putting the oral law into written form for the first time (it had been passed on orally from generation to generation since the time of Moses), so it wouldn’t be lost. And the wisest and most learned of their people began to meet in groups to discuss and analyze and interpret the Torah in combination with the oral law. Their discussions were recorded, and that is what became the Talmud of today. The people continued to lead a Jewish life, and that is what saved them.
When they were later allowed to go back to the land of Judea, they were still Jews. They built another Holy Temple and learned to live under foreign occupation for most of the rest of their history in their land. After the second Holy Temple was built, they returned to their previous ways where all animal sacrifices had to be made at the Holy Temple.
Perhaps the biggest change of all came when they revolted against their Roman occupiers and were utterly defeated. Again they were exiled from the land, never to return in large numbers for almost 2,000 years. During those times, they migrated to all parts of the Western world, most prominently North Africa, Spain, and all parts of Europe and Russia. Being in scattered communities, they learned to replace the Holy Temple with synagogues, and they replaced animal sacrifices with prayer services, and they replaced Priests with Rabbis (who were teachers and spiritual leaders).
Using this way of staying Jewish, they became very legalistic in their observances and were often isolated communities in a sea of Christians or Muslims. They were able to survive the Inquisition and the Expulsion from Spain in 1492 and they were able to survive countless expulsions and pogroms in Europe.
