IMO, the first thing to recognize with networking is that there are at least 3 tiers of people you know, with regards to their ability to help in your job hunt. Tier 1 are the people who know your technical ability, and can directly vouch for you being a good contributor in your role. These people are great to have, but new grads simply don't have them, for the most part. Most of the people able to directly vouch for their competency are their equally looking-for-work peers, or pretty distant from industry professors. Tier 2 are the people who know you well enough to assert that you're not an absolute pain to be around. They don't necessarily know whether you're a genius double-stack 12x developer or a codemonkey, but they know you're reasonably likeable. Then there's Tier 3, who don't know anything about you personally, but they know people who know you.

New grads (myself included, back then), tend to discount Tier 2, because in their head the hiring process is looking for the single applicant with the best technical skills. When in reality, it's a lot more of a "who can we get quickly, who won't have a negative impact on team output or morale". Parents, Parent's friends, friends, and friend's parents all can fall into Tier 2, and absolutely should asked about whether their workplaces are hiring, and if so, if they could provide a recommendation.

Tier 3 is mostly useful for finding out about positions that don't necessarily get publicized, but depending on mutual connection to the shared acquaintance, might be willing to offer a recommendation.

With regards to where to network, that comes down to engaging with social gatherings that bring together a spread of people that aren't exclusively your direct peers. That's the stumbling block a lot of new grads find themselves in, which is that all their social time is spent with other new grads (or worse still, nobody at all). Clubs, parties thrown by friends' parents, university alumni events, hell, join the Oddfellows (YMMV, some lodges stopped recruiting after Vietnam). Conferences, whether technical or not. Hell, a step I recommend for everyone is going to bars and talking to strangers. Not highest density networking opportunity (except some gay bars in SF), but it's a pretty good environment to practice casual communication with people you have approximately nothing in common with, with very low stakes.