Below is my answer to your question "How did you find work, when you started your career?"
My first several projects (at least!) were for people I knew or for people who were referred to me by someone I knew.
These days my website does bring me some work, but I think the majority of projects I work on can be traced back to someone I know. I have acquired some excellent clients thanks to volunteering at a local nature reserve and to being active in SONSI (sonsi.ca).
My advice to anyone who is looking for illustration work:
1) Be active in your community – though not for the express purpose of getting work. Volunteer, join clubs, be social, engage. Not only is it good for the soul, but someday one of those relationships will probably lead to work - and it might be in the most unexpected way.
2) While working on a project, don't fear asking for help from scientists or other content experts. The worst that can happen is that they won't reply; the best that can happen is that someone enthusiastic about the subject your illustrating is really helpful and now knows you exist and might hire you in the future. If they do help you, be sure to thank them with a card or print featuring your work.
3) Have a website and put as much good quality work up there as you can. Sometimes people will end up at your website after searching for an illustration of something specific. Do keep in mind that potential clients who find you via your website are likely to hire you to do the same type of work that they see in your portfolio.
4) Others might say to be active on social media. Personally I have not maximized the potential of social media, but I can say that (for me) Twitter is definitely showing potential (I just joined last month).