How is Federalism demonstrated in the legislation of No Child Left Behind?

You ask an excellent question!  In order to answer this, first, you must understand what "federalism" means.  In essence, under a federalist system, the state and federal government share power to make laws and provide for the citizenry.  

A careful reading of the Constitution reveals that there is no mention of public education anywhere in the document.  As a result, some people argue that, thanks to the 10th amendment, the job of providing for public education belongs to the states. (The 10th amendment reserves those powers neither given to the federal government nor denied to the states for the people and/or the states.)  However, there is also a clause in the Consitution, known as the "necessary and proper clause" or the "elastic clause" which gives Congress the power to pass any law that is "necessary and proper" for the governing of the people.  This is was allows the federal government to pass laws about public education.

So, thanks to the 10th amendment the states are responsible for creating much of the legislation about education in their own states.  (Incidentally, this is why different states have different laws about education, including rules about kindrgarten, truancy, and the legal drop-out age.)   And, simultaneously, the Congress can pass laws, like the No Child Left Behind Act, which also mandate certain education policies.  This is, at is essence, an example of federalism at work.