First of all, organizing things that others will enjoy is certainly a great way. But you also have to motivate people to bring their friends, otherwise you'll always be seeing the same people. People bring their friends when there is something they really want them to experience, so that's what you should focus on.
Also, meeting people is a great way to realize that you can outsource responsibilities to others, something that can actually "scale". Often this allows you to network to the right people. The key here is not to be perfect, and not to put too much responsibility on yourself. For example, you want to bring together two groups of people (men and women, say, or investors and entrepreneurs) that would really like to meet each other. You want to cultivate an aura of quality (i.e. the men and women are exceptionally attractive for whatever reason) and selectiveness in order to inspire people to perpetuate this selectiveness and recommend it to their friends. Suddenly the experience is created not just by you, but by this self perpetuating aura of exclusivity.
Being the facilitator and helping people meet each other actually gets you a lot of points, which you can use later when you need a favor yourself.
If you're coming as a guest, though, there is a real economics that starts happening, and a currency. Perhaps it is unfortunate from an idealistic point of view, but that's the way it works in many conferences, nightclubs, etc.
In general, though, if you want to come to events as a guest, you probably want to be invited either by the organizer or by a regular. If it's the organizer, you'd ideally like to bring some "high quality" friends to the event (such as fellow smart engineers) and introduce them to the organizer, so the organizer will want to invite you again.
Additionally you can form a little "group" that tells each other about events and invites each other. At these events, when you talk to someone important, you can tout the other people in the group instead of bragging about yourself, and they would do the same for you. As a result, you are able to meet many more people through your "network" who is out there meeting people in 10 different places and filtering them for you, because you yourself can be in only one place at a time.
How to start motivating people you know to start networking wherever they are and mentioning you when the opportunity comes up? You have to start doing it for them first. Ask for their business cards. You have to hook people up with opportunities and then ask them to go out and do the same for you. Give them your business cards.