You can network with virtually anyone, but you'll yield better results by honing in on someone in your field with more experience and power. These are the kinds of contacts that could evolve into mentors.
Know what you're looking for. If you want a mentor, focus on a notable person in that segment of the industry. (If you're hungry for a publicist position, find someone in that position.) Don't be afraid to use flattery to get what you want. You'd be surprised how well people respond to it! Bring a stack of business cards—but don't just hand them out to everyone. Be selective, and show your appreciation by having some appropriate talking points ready.