A mentor is someone who takes a personal interest in your success at learning and achieving your goals, and they’re in a position to help you do it.
Here's some advice from the Edupunk's Guide tutorial:
Look for real chemistry. Prominent people get lots of attempts to contact them, and you may not actually have that much in common with Oprah. You’d be better off finding someone who does what you want to be doing, whether worm compost or natural hairstyles. Look on Slideshare (slideshare.net), YouTube, Twitter and blogs to find the perfect person.
Reach out respectfully. The Internet age makes it easy to connect with people but that also means that people get many, many attempts to connect with them. I’ve found that the best way to connect with someone online is to ask a genuine question about his or her work.
Don’t be afraid to ask. Once you’ve exchanged a few emails or a phone call and established a real conversation with someone, you can ask them for a favor: to take a look at your learning plan or portfolio, to let you know about summer internships in that field, or even more broadly, to stay in touch and answer your questions. People like to feel helpful.
Mentoring is a two-way street. Don’t forget that as a less experienced person with enthusiasm and energy, you have something to offer your mentor as well. Maybe it’s research help, or help with a project. Maybe it’s just a younger person’s insight into a situation. Offering to help will let your mentor know that you appreciate them.
Go long and short. Classic mentorships will last for years, but you should also be alert to the opportunity to gain wisdom, good advice, and valuable connections in just one conversation.
Mark this task complete once you've found a mentor. In the meantime, tell us about your experiences reaching out to possible mentors.