Having the correct shoes is the most important thing for a ballroom class! Steer clear of rubber soled shoes. See the apparel section for more information.
Technically you should dress like you’re going to church! Women are usually expected to wear dresses or skirts. You want something flexible that will move with you as you dance. Men can wear a dress shirt or polo shirt and slacks or khakis. You want to steer clear of wearing denim jeans if possible as ballroom classes are more formal! Your hair can be fixed however you want as long as it doesn’t get in your way. Be mindful however if you have long hair and you pull it back into a ponytail because you don’t want to smack your partner in the face by accident!
If you are taking class just for fun then simply get a pair of your favorite heels with a strap and just make sure they are comfortable and not too high. Ballet flats work just as great too if you don’t want to wear heels for over an hour. Guys can wear Sperry’s if they don’t want to pull out their dress shoes but definitely steer clear from tennis shoes or flip flops.