Short answer: States have constitutions as well. The Constitution is the overall guiding document for the Federal government; state constitutions are foundational/guiding documents for the components that make up the United States.

A good way to think about the US is as a more federalized EU, after several centuries and a civil war to figure out how power devolves between the Federal and State governments. The individual states were originally sovereign entities, bound together through a very weak system called the Articles of Confederation. After this was shown to not work very well, a group of legislators committed treason against the government outlined in the Articles, and convened to write the US Constitution, which the sovereign states decide to adopt after furious debate.