I have been a firm believer in that networking is not about collecting business cards, being at every meeting worth its name, accosting every member of a club/student body / professional group or knowing (the names of) more and more people.
Networking starts with working on oneself. One has to be able to add value to others to become acceptable in a network. To be able to add value one needs to know more about at least one thing (anything!*) than others can know. To be able to let people know that one has some value to add, one has to participate in meetings & parties; take every opportunity to speak in public; take some position of leadership (need not be formal). People will orbit around those that have gotten recognized as someone who can add value (through special skills or position).
Networking, at its best, is when people want to get in touch with you; not necessarily when you want to reach out to people.
PS: * You can even know a person who can make a difference