If you have a science education but are not an active researcher, then you most likely do not have access to the same communication resources that university staff have. This does not mean that you can not become a science communicator. Quite opposite, actually.
There are many ways to work with science communication outside the academic environment. You can work at a university or company as science communicator. These job types are getting more and more common with the increased need for science communication in the public space – partially to counter the pseudo-science environment and partially to inform the general public about their work.
You can also go solo and start up your own science communication universe. If you are interested in journalism, there are ways to go to learn the basics (courses and so on). You can also contact a science publisher and her how the process is. Most publishers are always on the look-out for new talents and why should this not be you.
If you want to start here and now you can start building your online presence by creating a website, social media account and so on to attract followers that you can engage with the science you choose to convey.