This is such an undervalued and under-utilized way of meeting new people. Everybody knows someone. If you want to meet someone in particular, ask the people you know if they know anyone who knows the person–and then ask them to make an introduction.
At the end of the day, a warm lead is always better than a cold lead. If you can get in the door with some sort of referral, even if it’s, “This is a friend of a friend of a friend and I think you two should meet,” that will always be better than a cold email or phone call.
That said, it’s important that you not over-ask, and reciprocate whenever possible. For example: I know quite a few people who have very expansive networks. They have direct access to some very powerful people. At the same time, they know the value of their network and do not share it lightly.
If you want to take advantage of other people’s networks, it’s on you to build your own. You can’t constantly ask for introductions if you don’t have something of equal value to share. That’s your job. Build your own network so that when you ask for an introduction, the person you’re asking feels comfortable doing so because she can trust you with her relationships and she knows she can count on you to reciprocate when you can.