Ask HN: How do you build genuine connections while you also badly need a job?

There is a book on personal networking that is titled "Dig your well before you're thirsty." It's an interesting saying, to be sure. Paints a good analogy of avoiding desperation from procrastination. But there is also the saying, "The best time to plant a tree was 20 years ago. The second best time is now."

When the job situation is more dire but you don't have that good of a network, how do you avoid making people feel used, while also considering the time-sensitive urgency of your job situation?