3:2a Then Jeshua son of Jozadak and his fellow priests, along with Zerubbabel son of Shealtiel and his associates,

Then Jeshua, the son of Jozadak, and the other priests, and Zerubbabel, the son of Shealtiel, and his colleagues/associates
-or-
Then Jeshua, ⌊the high/leading⌋ sacrificer son of Jozadak, and his companions who were also sacrificers and Zerubbabel son of Shealtiel and his companions ⌊started working⌋.

3:2b began to build the altar of the God of Israel to sacrifice burnt offerings on it,

began to build the gift/sacrifice place of their God. They did this in order to give/offer completely burnt sacrifices on it,
-or-
They began to rebuild the place/platform for entirely burning animals/sacrifices for the God of ⌊the people of⌋ Israel.

3:2c as it is written in the Law of Moses the man of God.

according to what it says in the Law that God had given Moses, the man of God.
-or-
⌊They wanted to do all of this⌋ in just the way that Moses instructed them. Moses was the man that God had chosen ⌊to serve him and to write his instructions⌋.

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