You can make a ritual related to the blue moon, you can charge moon water during the blue moon to give it an extra kick, there are other esabat related rituals that you can alter to match the blue moon, but it is really up to you.
for the last blue moon i had done a ritual that was related to wishes. for this you need two champagne glassess. (one for you and one for the earth, goddess, universe, etc.)
start out by making a list of things you wish you could have, or wish to happen. contemplate on this list and cross out the ones you dont really want, all but 13. then on parchment, cut out 13 crecent moons. Write each of your wishes on its own moon. When this is finished, use safety pins to pin each crecent on one paper. Fold this paper 9 times and bind it with a gold ribbon. Go out side and sit with the full moon. Pour the glasses with champagne as a symbol for celebrating the moon in its entirety, (or juice/ water if your underage.) Focus on your intent, to have these things/happen.
Raise your glass and "Toast". But first pour the Earth's glass into the ground. (its respectful.) And then drinking your own.
Present the list to the moon and speak of true love and intention. Speak from the heart on this, it only has to be as fancy as you want it to be. But showing of your true self is always the best way to go.
Always thank the deities if you've invoked any, and always thank the spirits.
From my experience ive had very well results. but as always. do be careful what you wish for. And always make sure its what you truly want.