All institutions are different, but most likely you will have access to a communication department or press office at the university level or within your institution. Working with communication teams should be like a symbiotic-relationship, their goal is to help amplify the interesting stories occurring at the university, or in your department, and you are the provider of those stories. Talk with the university news office and articulate your communication goals, and they can explain the steps you can take to reach your audience, whether through a news release about a publication, or a broader story or blog post about the subject of your research. Build a relationship early in your research process and continue it throughout your project.
SESYNC is funded through an award to the University of Maryland from the National Science Foundation. These are two additional resources you may want to consider utilizing as your research progresses. Additionally, non-academic institutions often offer support for communicating science, for instance, AAAS has many great tips for sharing your science.