Using a mentor is a two-way street. Mentors are usually happy to give to you, but if you're smart you'll give something in return. Although many mentors want little more than the opportunity to give back, or information you have about your world and your team, it's always wise to figure out what you can give back and take action.
Toddi Gutner, writing in the Wall Street Journal about mentors for Gen Yers had a number of helpful suggestions. She pointed out that you're much likely to get a mentor's support if you show that you understand the manager's pressures--especially in today's grim economy. In addition, approach your mentor in a way that offers help. "You can tell a respected manager that you admire his work and ask him to coach you on specific things like how to close on a big sales deal or how to engage colleagues on a project. In return offer up a skill you have to help on a project he's responsible."
With your GenY knowledge of technology you might also consider teaching your mentor how to use Twitter. Or, set up a page for him/her on Facebook, or show him how to get the most out of LinkedIn. Just remember, mentoring and networking run on reciprocity: You scratch my back and I'll scratch yours.