A bill is born by a Congressman or Senator introducing an idea for it. It might come from an interest group, the executive branch, or the constituents. The process begins with the legislature introducing the bill.
The bill now goes to the committee. Except for revenue bills, the bill has to start in either the House of Representatives or the Senate. The bill goes to the committee that it applies to, and if the majority approves, then it goes to the full Senate for a vote. If the bill receives the majority of the votes, then it moves on the the House of Representatives. Before they go to the House, they must go to the rules committee. The rules committee is a group of legislators that report bills.
Then the rules committee reports the bill to the House. If the bill receives the majority of the votes in the house (328+) it passes. The bill has to pass both houses before it can go to the President. This almost never happens. The second house to get the bill will want to change it, so then it goes to a conference committee. They are a group of people that are from both houses and resolve any arguments or disagreements on the bill. They then send the bill back to both houses for another vote.
Now, the bill has to be voted on by both houses. If the bill gets the majority of the vote from the House and the Senate, then it gets passed to the White House.
There, the President can sign the bill and make it into a law. He can veto the bill also. There is a 3rd option though... If the President neither signs nor vetoes the bill, in the following ten days, congress goes out of session and the bill doesn’t really become a law. That's called a pocket veto. If congress really wanted a bill to pass and the president vetoed it, they can override it by getting a 2/3 vote in both houses. But this doesn't happen that often. Then the bill becomes a law.