Good answer, Matt, it is definitely the best way to work.
I'd also add that these personal recommendations of course only come from being seen to do great work, and fostering those relationships carefully. It's very easy to become competitive, especially when young, but that competition can impact a good relationship if not handled well.
For a great, and entertaining, read on this I'd recommend the excellent Chris Hadfield's "An Astronaut's Guide to Life on Earth", and especially his concept of being a "Plus One" - making sure you help other people, and in return they will help you.
That's key to getting these relationship-based referrals.
Best of luck!
Networking is absolutely critical as you head on your career journey. Of the substantial jobs I've held over the last 25+ years, only my first job was done by applying and passing exams, oral boards, etc. Every other significant position I've held is because I was referred by someone that knew me, my work, talents, and drive to succeed. To be honest, there is a lot of luck involved; I know if I hadn't met certain people at the right time, I'd never be where I am now. However, it's not all luck.
For example: How I got a job at Google:
-- I left Walmart.com for a job with BEA Systems because of a referral from someone I knew at Walmart
-- At BEA, I met a colleague, Craig.
-- I left BEA, to join another tech company, on the recommendation of a VP that I knew from working together at Walmart
-- I kept in touch with Craig
-- 2 years later, he referred me to a job at Postini
-- 2 years later, Google bought Postini, and I've been at Google ever since
Was I lucky? Absolutely. But I put myself in a good position with strong networking skills.
How do you go about improving your network? At school, join clubs that interest you, get to know other peers by working on projects or study groups together. Stay in touch with them; make that effort. In the working world, seek out those who have the job you want. Ask them if they would be willing to share ideas. Find colleagues you enjoy working with and make a habit to contact them periodically; half of networking is not losing track of people once you've made that connection.
There are some people where I only have lunch with a few times a year, just to keep the relationship alive. Once you build out a mature network, you can make a phone call and get your next job.
Hope this helps. Best wishes to you!