These standards are to be applied statewide. Textbooks and other materials are designed with those standards in mind. Teachers are instructed in how to teach to the standards. Students are then tested on those standards toward the end of the school year. Depending on the state and district, those tests may be an off the shelf test, such as the Stanford 9 in California and Texas, or a state-made test.
Some states supplement the multiple choice tests with writing samples and other assessments.
The results of those assessments are looked at very carefully and often consequences, positive and negative, can be assigned to school districts, individual schools, teachers, and students. The nature of the consequences depends on the state. In Florida, for example, students from failing schools can receive vouchers for private schools. Schools are expected to grow in their API numbers and get special money if they do. Schools who don't are subject to more intense supervision.