In contrast, the ideal candidate is passionate about whatever job they're going for. Make lists of companies that you would love to work at, and pursue them directly, whether there's a job listing open or not. Recruiters use LinkedIn to find candidates all the time... it is just as valuable for new grads just entering the workforce.
When pitching for startup funds, there's a saying: When you ask for money, you get advice. When you get advice, you get money. This applies to jobs too. People love talking about themselves and what they do. Luckily, if you're new, you stand to gain from that, and massively.
Finally, it pays to be prepared for interviews. I was just having dinner with a friend who's a producer at the biggest name game studio out there -- he was just complaining about how he'll ask if the candidate has played _____ game, and it'll be to the level of 'I tried the demo.' Trying the demo isn't good enough. Becoming a Level 32 Dwarf or thereabouts is probably what it takes, at least for this example.
Hiring managers, no matter what field, want to know that the person in front of them is a) smart, b) gets things done, and c) would love more than anything to work for them.