I echo much of what Lisa said. I got my BA in English and my MFA in creative writing and I also write science and technology pieces. Sometimes it's a bit of an uphill battle--reading articles in scholarly journals takes me hours because I have to be sure I'm understanding all the references, which means I often need to look things up, etc--but it's doable.
Arguably the most important aspect of science writing is being able to communicate in a jargon-free way to mass audiences. Most people don't really understand emerging technologies or their implications, so if you can help them to understand not just what's going on, but why it's important, then you can write about science. Doing this involves more critical thinking than specific knowledge or training about science. There are a number of science outreach positions (for science festivals, nonprofits, even university departments) out there that involve communicating to audiences both young and old. These are good places to start a job search.
You will need to build up clips that show you can write about science, though. I did this through a blog I started a number of years ago, which gave me practice writing about scientific topics of my choice in a low-pressure environment. Once I built up a bunch of blog entries, two important things happened: I had clips to show other publications and I started figuring out what type of science and technology I wanted to cover. It's unlikely that you'll be writing about everything with regards to science, so developing an area of focus (climate change, the effects of social media, genetic modification, etc) really helps, especially because you end up learning a lot about the science itself and that knowledge makes for increasingly insightful articles.