The University of Washington Center for American Politics and Public Policy has designed Legislative Explorer (or LEG/EX) to help with this!
After launching LEG/EX, you can select a particular session of Congress. By selecting Play, you can watch an animation of bills being introduced and moving to committees, to the other chamber, and to the President. You can also limit to certain types of bills such as by political party, a particular Senator or Representative, by subject and much more.
Visualization of bills introduced by Maryland's Representatives in the current Congress.
Each colored dot is a specific piece of legislation. If you hover over that dot, you will learn more about it, and be given a link to more information at Congress.gov!
Information is available back to the 93rd Congress (1973-1974). Take a look and you just may be able to gain a better understanding of our legislative process!
Of course, it never hurts to rely on a classic to help you understand the U.S. lawmaking process, either!