If doing something that makes you feel delighted, cheerful, or full of glee, you can say you do it joyously. When your math club won the big state competition, your team celebrated joyously.
Joyous means "full of joy," and when this feeling goes along with some action, that action happens joyously — whether you're laughing joyously at a funny movie or running joyously to meet your new puppy. Some synonyms for this adverb include gladly, cheerily, and blissfully, but none of those quite capture the exuberance of joyously.