For a bill to become a law it starts in a committee in either the Senate or the House.
The president can pass or veto the bill. After 10 days, a bill passed by Congress automatically becomes a law if the President doesn't act and the Congress is still in session. After 10 days, if the President doesn't act and Congress is not in session then the bill is automatically vetoed, this is called a pocket veto.
If a bill does not pass it can be sent back to the committee for changes and then voted on again.