FORTUNE — Dear Annie: I’ll be graduating from college at the end of May, and although I’ve had interesting conversations with campus recruiters at a career fair and been interviewed afterwards by four of them, I haven’t gotten a job offer yet. I know that each of the companies I’d like to work for is interviewing a lot of people, but I think my chances are pretty good, because I have a 3.8 GPA, have been a leader in campus activities (currently president of the Student Union and captain of the lacrosse team), and have done two solid internships, with excellent references.

Even so, my impression is that everybody else who gets to the interview stage — my roommate, for example — has a very similar resume. Do you have any advice on how to stand out? What do employers really want? —Pick Me

Dear P.M.: Great question, especially since most of the answers apply not just to new grads, but to anyone who’s looking for a job. First of all, although your 3.8 GPA is impressive, it isn’t as important to employers as you might suppose. “One thing we look for is a strong work ethic,” says Alexa Hamill, who is in charge of campus recruiting at PwC. The firm expects to hire more than 4,000 new grads full-time this year, along with about 3,500 interns.

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“Good grades do show you’ve worked hard at your studies,” says Hamill. “But we’re really looking for people who are well-rounded, and who have a passion that they have stuck with and developed that is outside of ‘book learning.’”

Your extracurricular bona fides suggest you can check that box, but here’s an essential question: How well can you describe what you’ve achieved, and how it might apply to the working world? “Year after year, one of the biggest difficulties I see in applicants is their communication skills,” says Dylan Schweitzer, Northeast head of talent acquisition for Enterprise Rent-a-Car, which hires more than 8,500 new grads annually for its management training program.

“Many people coming out of college have had great activities and internships, but often we find they’re unable to explain what they’ve done,” Schweitzer observes. “I’m looking for someone to say things in a positive way, who is excited about what they’ve accomplished so far, and who sees the failures they’ve had as learning experiences, as opposed to obstacles.” Alexa Hamill agrees and adds, “This generation is used to communicating online but often not as effective in face-to-face situations like job interviews.”

The solution to that problem, she says, is practice, and asking for feedback: “Rehearse what you’re going to say about your experiences with as many people as you can — a friend, a parent, a professor. Try to practice with a wide variety of people, because you’ll get different feedback from each one.”

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A few other suggestions on how to wow interviewers:

• Be persistent. “Job hunters who want an edge over other candidates today need to engage employers in multiple ways,” Schweitzer says. “We’ve had applicants meet us at a job fair, then connect with us on LinkedIn, call our offices, and send us emails.” That may sound pesky, but Schweitzer says not: “The people who make a serious effort to get my attention show me they’re willing to go the extra mile to accomplish tasks.”

• Remember, it’s not all about you. Schweitzer says that, when an interviewer asks why you want to work for Acme Corp., “the proper response is, ‘I’m a hard-working person with experience in [fill in the blank], and here is what I want to contribute.’” Too often, he says, applicants’ responses are “all about them, when it needs to be more about their connection to my organization. Tell us what you bring to the table, not just what you want.”

• Research each employer thoroughly. Just taking a look at the company web site won’t do it. “When I ask candidates what they know about us, it’s rare that someone tells me something that isn’t on our web site,” Schweitzer says. “A person who researches the company and mentions something else about us is someone who stands out, because he or she has done more than the typical applicant.”

• Emphasize your leadership skills. “Not everyone we hire is a 4.0 student with a perfect resume,” says Schweitzer. “The person who is willing to work hard and put in the extra effort is going to come out ahead. For example, a military veteran with a 3.0 GPA but who has experience leading others, and is used to hard work in extreme situations, is often a better candidate than a 4.0 student who is unable to demonstrate those qualities.”

• Polish your online presence. When prospective employers Google you (and they will), you want them to be impressed by what they find. “A candidate’s online image is so much more important than it was in the past,” notes Alexa Hamill.

Creating the right persona in cyberspace these days goes way beyond just keeping your frat-party photos off Facebook. To help you do it right, PwC has put together a detailed (and free) online tutorial on building your personal brand, including a workbook that will walk you through it step by step.

Incidentally, since you mention that you’ve already had four interviews with recruiters, it might interest you to know that the average wait between interview and job offer is 24 business days, according to the National Association of Colleges and Employers. Companies in some industries take longer — 30 days in engineering services, for instance, and 39 days in hospitality. Computer manufacturers are the quickest, taking just 16 days to ask when you can start.

Talkback: How did you get your first job out of college? If you’re a hiring manager, what makes an entry-level candidate stand out? Leave a comment below.