After 48 years in captivity in Babylon, Israel is finally able to return to the promise land. Shortly after their return they began rebuilding the items of worship needed to worship God. They start with the altar on which sacrifices were made. The passage says, "Even though the people were afraid of the local residents, they rebuilt the altar on its own site" (Ezra 3:3). The people who resided in Israel while Israel was in exile likely put an altar of worship to their own gods where Israel's used to be. Tearing down their altar to replace it with their own would probably make those residents angry.
During this time they were also celebrating the Festival of Shelters. For this festival they would create temporary shelters and live in them in remembrance of their time in the wilderness in which they lived in tents. This was good timing since they were just coming back from exile because of the work of God this festival would have a even more impact then previous festivals.
The man over-looking all this was Zerubbabel, an Isrealite who was appointed by King Darius as the governor of the area. He also just happened to be part of David's family line. He overlooked the rebuilding of the Temple. He was able to get away with this because there was mass revolutions during this period of Darius' reign. Since he was so distracted stopping those revolutions Zerubbabel was able to work under the radar.
With the altar done they began to lay the foundation for the Temple. Once the foundation was laid they worshipped God with mixed reactions. Those who had never seen the original Temple were filled with joy at their new found freedom to worship their God. Those who had seen the original Temple wept. The foundation for the new one showed that this Temple wouldn't reach the glory of Solomon's Temple and they wept at how far Israel has fallen.
Although they now have returned to their promise land they were not completely free. They were still under the rule of Persia and eventually would come under the rule of Rome. It was under this rule that Jesus would come.