My answer is for the United States.
Briefly, the bill has to pass both the Senate and the House of Representatives and it must not be vetoed by the president. That is how something becomes a federal law.
A state law is much the same way except the governor takes the place of the president. If there is only 1 house in the state then it goes from the house of representatives to the Governor who has 10 days to veto it. Nebraska is the only state without a senate.
