How important is networking? How do you get good at it?

A recent post by Daniel Levy brings up the topic of networking, especially regarding job-hunting:

While the preceding paragraphs emphasized the value of a strong education, they did not focus on skills important to finding and maintaining employment. Among the most important is networking. Sure, while social groups such as Facebook, Linked-in and Twitter can provide some resources, the greatest networking activities involve face-to-face introductions/conversations. These must also be accompanied by diligent follow-up...

[snip] In closing, most of one's success will always depend upon a strong knowledge and skill base.  However, There is always a component that directly relates to who one knows and what opportunities are available at any given time.  The value of networking will not always be immediately recognized - but when it pays off, the dividends are usually significant.

This reminded me of a couple of posts by Lisa Balbes over at the ACS Careers blog, which lay out what that "diligent follow-up" might look like. To wit:

One way to test this is by looking at your list of connections, and asking yourself “Would this person take my phone call?” An even better question – “If I lost my job and called this person, would they merely sympathize, or would they go out of their way to look for leads and opportunities that matched my background and professional goals?

To turn it around, how many of the people in your professional network have you talked to lately? How many have you done a favor for, or passed along a tidbit that you thought might help them out? How many do make contact with on a regular basis? Or do you look your list of connections and try to remember where you met them, and why you wanted to connect in the first place? [snip]

For people you haven’t talked to in awhile, make contact. Send an email, write a card, or pick up the phone.

As I am relatively early in my career, I'm not quite sure what "good networking" looks like. At the same time, it seems to look like being a friendly, helpful person who remembers people and cares about them. I think the internet makes that sort of thing relatively simple; e-mails and LinkedIn notes aren't too fraught with nervousness, even if you're the world's most awkward, introverted person on the phone or face-to-face. As Levy notes, I'm hesitant to say that it's the cure-all for a tough time looking for work, but it can help.