Pay special attention to the overview of the legislative process, introduction and referral of bills, and committee consideration sections (first 12 minutes of the video playlist) and to the executive business in the Senate, resolving differences, and presidential actions sections (last 7 minutes).
National laws are made in Congress, which is part of the legislative branch and is made up of the House of Representatives and the Senate. Laws that are made by state legislatures (like the GA General Assembly) have a completely different process and are not included.
Sponsoring a Bill
All laws in the US start out as a bill. A bill is proposed legislation, usually sponsored (i.e. written) by members of Congress. There are several steps that a bill must go through before it becomes a law.
A bill can originate in either the Senate or the House of Representatives (with some exceptions).
First, a senator or a representative and his staff write a bill, which is called a draft of the proposed law. The bill will be introduced in either the Senate or the House of Representatives and a copy will be passed out to each Senator or Representative and assigned the appropriate committee to study the bill. Bills coming from the Senate have the prefix "S." on them, and bills coming from the House of Representatives have the prefix "H.R."
Second, the bill is then sent to a Standing Committee (a small, permanent group made up of legislators who studies and reports on bills) reviews the bill and does one of three things:
1. Sends the bill back to the floor with no changes.
2. Makes changes and sends it back.
3. Tables the bill -- In other words, they can do nothing and the bill effectively dies for that session.
Not all bills introduced in Congress make it to a vote by all members of Congress. Many bills only get to the committee stage.
Committees in the course of researching and studying the bill may call experts to testify at hearings before the committee. Congress can also call hearings with no legislation attached to study issues important to the country (or Congress), such as Doping in Sports, the Financial Banking Crisis, etc.
If the committee sends it back with no changes, then the bill goes on the calendar to be voted on by the Senate or House. When that day comes, the bill is voted on and if over half vote yes to pass it then it moves along to the next step.
If the bill is passed by one branch of Congress, it then moves to the other branch of Congress. The Bill goes through the above process again in the second branch of Congress.
During the whole process amendments are added and changes are made to the bill in committee and on the floor of the Senate and House. Thus by the final vote the bill may have gone through several revisions and look different from the sponsored bill. If enough changes are made by the committee to the bill, then it may be resubmitted with a different H.R. or S. number. Keep this in mind when tracking legislation.
If the bill is passed in both the Senate and House, the bill goes to the President. If the President signs the bill, it then becomes a law. It may also become law if the President does not sign it for 10 days. If the president rejects (vetoes) the bill, it can still become a law if two-thirds of the Senate and two-thirds of the House then vote in favor of the bill. Very rarely, however, does a Congress have the votes to overturn a Presidental veto.
ProQuest Congressional allows you to track recent bills (1989-present) through Congress. Click on "Legislative Histories, Bills and Laws." The best way to search is by bill number by clicking on the "Get a Document" tab, and indicating "Bill Tracking" on the drop down list.
Having problems linking the popular names of laws to the bill / P.L. number? Wikipedia is your friend.
Here is a helpful diagram of the process. ProQuest Congressional has an indepth explanation as well.