It used to be that most students sought out internships between their junior and senior years. However, these days many students complete 2-3 internships during their college careers. In fact, some schools require the completion of at least one internship prior to graduation. These students will be your competition for the best jobs and spots in graduate school! Typically, the prestige and responsibility of internships increase with the level of skill and experience you are able to offer a potential internship site. Therefore, it is helpful to take more "entry-level" internships early on in your college career. Consider a part-time internship during the school year or the summer after your first year. You'll find it easier to get more competitive internships later on as you gain experience and have taken more college-level courses.
MANY INTERNSHIPS HAVE EARLY DEADLINES! For example, if you want to work for a government organization such as the FBI, CIA, or State Department, applications are usually due in September or October for internships the following summer. This is done because you will have to pass several security checks. Similarly, most major corporations, at least for their best internships, have deadlines in November or December. This does not mean that you cannot gain an internship if you begin looking in March. It just means that it is less likely that you will get a nationally recognized internship. We have had success in gaining internships as late as May, but you're much better off if you start the process early.