Communicating sophisticated and technical ideas in a way they can be understood to a public audience is tricky.
1. Use metaphors - try to connect scientific ideas to ideas that people can relate to from their everyday life or common knowledge.
2. Draw pictures - draw your own pictures and label exactly the features on them that you want to bring to your audience's attention. Even better, draw and label them in real time as you explain concepts to them (make use of animation or speed-up footage).
3. Imagine you are speaking to a younger sibling or older relative (who is not a scientist) - imagining a non-scientist from your own life to whom you are speaking will help you avoid using terminology you've grown accustomed to using with your science classmates but is unfamiliar to non-scientists. It should also help you think about how to break down sophisticated concepts into bite-size pieces. At the same time, you don't want to oversimplify, your relative is intelligent, they just don't happen to (yet) be a scientist. The real art of science communication being able to explain sophisticated ideas, in all their complexity, in plain language.