Hi there!
Bills go through various steps and change hands many times before they can pass through Congress and go onto the president for approval (or veto).
First step: Bill is introduced in the House or the Senate.
Second Step: Bill is passed to the proper committee for reviewal and possible changing. The bill can also be shut down here resulting in it never reaching a vote. If it passes the committee/subcommittee it belongs to, it is marked on the Senate/House calendar.
Third Step: The full House/Senate vote on the bill and if both house of Congress pass it, it is sent to the president for approval or rejection. From there, Congress can override the president's veto by a 2/3 majority vote by both houses.