Most schools still require students to take either the SAT or ACT. These are usually taken in the spring of junior year and, if desired, again in the fall of senior year. The PSAT is offered from 9th-11th grade and provides feedback on performance (the SAT and ACT do not). The PSAT also offers scholarships for students who excel on the exam when taken in the fall of their junior year.
These resources can give you an idea of what kinds of scores are needed for highly selective schools.
If standardized testing is not a strength for you, these lists can help reassure you that some schools are aware that these tests don't actually say a lot about whether a student will succeed in college.