I'm on a first name basis with well-known engineers high enough to shrink the formal HR process at Google, Yahoo and Facebook. If I asked to interview with them tomorrow, they'd put me in the process immediately, in an expedited manner. I'd probably go straight to the on-site interview.

I'm not bragging about this, because it really wasn't difficult to do. I didn't go to school with them, and with one exception I met them all after they had joined their companies.

Cold-emailing influential people, or introducing yourself to them at meetups, or any one of the myriad other ways to meet people applies in this situation.

Just be genuine, and network with them long before you'd ever want to call in a favor, this way you actually have a relationship with them. It also helps if you share something in common and actually have something to talk about, and if you want to connect with them for the sake of having smart colleagues, not just influential friends.