Networking with homeschooling groups, teachers, principals, substitute teachers and other tutors who teach things besides science is a great way to start getting referral traffic. Set up a simple website offering your services and then advertise on Craigslist and the massive amount of freelance work websites for direct internet search traffic. To get work, you can also join tutor.com or similar tutoring website, but they're not your clients at that point.
Your client will be whoever has the money, so you'll want to keep close relationships with them. They'll also be your best source of referrals. You should also mail them tangible bills either before doing the work or shortly afterwards, depending on your style and level of trust.
To build your reputation, you should take any qualifying or certification tests, as well as write as many scientific articles on topics you'll be tutoring in respectable places.