For five years I co-authored a blog called Math Munch, a weekly digest of the mathematical internet. I began writing it for my own students when I was teaching middle and high school math. Math Munch aims to make the brilliant, fun, colorful work of mathematical people accessible to a wider audience—especially young people—by curating great pieces of math that we've found on the internet.
I have helped to organize several Julia Robinson Mathematics Festivals.They are wonderful opportunities for young people to encounter mathematics in a collaborative, no-pressure, and fun environment. Check to see if there's one in your area soon, or help to organize one yourself!
I have also been involved with several math circles in New York, New Jersey, and the Emory Math Circle here in Georgia. Math circles are another great way for young people to access math outside of school. Find a math circle near you!