There are a few things I look for from an applicant:
Most important point with a resume: write like a real person would talk! Using 'magic' HR phrases like "motivated self-starter" usually get the application rejected. I want to hire a human being, not just a good actor.
A cover letter written specifically for our company! This should show that you know something about our company and internship program, and where you'd like to fit into it.
The internship application. You'd be amazed how often this gets ignored. Read the instructions for applying for any internship thoroughly, and follow them to the letter. If they want you to fill out an application, fill it out.
On that note, if there's a field that says "signature", print the form off, SIGN IT, and scan it in (or else use a tablet to sign). Typing one's name in a script font is not legally binding, and yes, we'll know. (That happened.)
References from former employers, supervisors, or professors (just have these on hand.) Family and personal friends don't usually count for this.
A portfolio of code you've written — GitHub is fine for this — just to show that you know some basics of coding. Don't worry if it isn't technically advanced or overly impressive. I'm mainly concerned with a personal dedication to quality, a consistent style, and the ability to problem solve.
Politeness. Just because we're moving towards a more informal society doesn't it's okay for an applicant to get chummy with me right off the bat. In emails back-and-forth with applicants, I should be addressed as "Mr. McDonald" until I give the cue to switch to first-name basis.
I usually let applicants off the hook for a "Hi Jason" in the first email, but if they don't pick up the social cue from my responses always starting with "Dear Mr./Ms. So-And-So," and ending with my full name, they're out of the running.
That last point may sound pedantic and overly fussy, but I've learned that if someone cannot use polite formality with a potential superior when applying for an internship, he or she is not likely to have respect for said superior in a work relationship.
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