While looking for information on the branches of government today, I found an excellent and thorough explanation of how a bill becomes a law on the USA.gov website. I was even more surprised that the document was written in easy-to-understand English!
How Our Laws Our Made is a 65-page document that explains succinctly how the members of Congress are elected, how each branch functions, and how a law is made from it's first idea to final approval at the President's desk.
While there are some rather lengthy sections that detail all the ins and outs of committees and such, the great bulk of the document offers concise explanations of the legislative process. If you're teaching your children about the U.S. government, this would be an excellent additional to your lesson plans.
You can see the table of contents of the document here. But instead of wading through the table of contents, I'd suggest just downloading the entire PDF and printing out the sections you'd want to read aloud.