When I was at PacBell I frequently had requests for help from people at my current employer. I had no real intent to leave PacBell. When I decided it was time to go, my current employer hand carried an offer to my door. It was acceptable and essentially locked down a new position about 10 days before I left PacBell. That was 1991.
Landing the first position before you have any track record or opportunity to network with people who know your skillset is difficult. Many students intern at my current company while they are in school. It gives them work experience, a chance to build a track record and a set of references with people who know what they can do. I've had an intern on my railcar project for 6 weeks each of the past two summers. A bright student from MIT. He worked on some signal processing algorithms to convert Matlab code and some numerical recipes algorithms into a first draft of C language versions.
Share the ones you remember now!