You first have to get into a PhD or PsyD program in clinical psychology. Predoctoral internships are arranged through these programs, and are typically completed during the final year of the curriculum. PhD or PsyD students typically complete four years of graduate courses, research, and teaching prior to their internship. During this time, they also complete a thesis and dissertation.
To be competitive for highly ranked pre-doctoral internships, you need to have outstanding grades, clinical skills, research experience, and recommendations. Students from clinical psychology programs all over the country are competing for these select positions, so you really have to stand out. Graduate training is tough, but you have to rise above your peers in any possible way in order to secure a top internship position. This is important, as internships usually lead to postdoctoral fellowships, which, surprise, surprise, are also incredibly competitive to secure. From what I have heard, having articles published in APA journals is a big plus.
As you may know, the real challenge is getting into a PhD or PsyD program in clinical psychology. Most programs receive well over 500 applications and only accept 5-10 students. Undergraduate GPA, GRE scores (General and Advanced Test in Psychology), research experiences, clinical experiences, and extracurricular involvement weigh heavily in the admissions decision. Publications are HUGE. A common mistake is for students to apply to clinical psychology programs straight out of undergrad, with little to no research experience and zero publications. A better choice is to work for 1-2 years in clinical research, get your name on as many publications as possible (try to get first authorship), and then apply. Not only will you gain valuable research experience, but you will also get letters of recommendation from your supervisors.
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Cheers,
PH