This is a really great question. I started applying for internships during my sophomore year of college and really had no idea what I was doing. I did not know too many people who were applying where I was and did not know who to ask. Despite this, I managed to get three great internships with the federal government two of which were overseas. I think the key to getting an internship is tailoring your resume to the position that you are applying to. Many people use the same resume for every job/internship that they apply to without modifying them; this is a huge mistake as you should highlight aspects of your resume that pertain to the job you are applying for. If a job description talks a lot about project management experience, highlight times were you displayed skills in project management on your resume.
If it is allowed, write a cover letter for the job to show that you are willing to go above and beyond the call of duty. Even if the job does not require it, cover letters go a long way of demonstrating how badly you want the internship and are a way of differentiating yourself from the others who are applying. Be sure to tailor your cover letter, like your resume, to the job that you are applying for. A common mistake is using the same cover letter for each job and forgetting to change the name of the company (i.e. applying to J.P. Morgan Chase but writing "Dear Well Fargo"...not good).
Almost all internships are applied to online and you need to be sure that you answer all the questions and be sure that the answers are accurate. You don't want to accidentally give them the wrong address and miss out on an internship offer. Don't skip questions and don't lie either, it's just not a good idea and starting off based on a lie is not good. If there is an essay question as part of the application be sure to be thoughtful and treat it similar to how you treated your college essay. The essay portion is often a key part of the application as it is whether the decision to accept/reject you is largely made.
What a great question! I have posted an article below that gives several tips when looking for internships. Always have someone, preferably a professional , review your resume. A recruiter will reject your resume very quickly if it has too many errors. Also, the cover letter is a great way to make yourself stand out and show that you are the best person for the position. It gives you a chance to link your education, and any previous experience with the qualifications of the position. Lastly, practice interviewing. Many school career centers offer mock interviews, these are vital to interview prep! I highly recommend these as they will help you become more comfortable with the process.
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