How can an art major with zero experience and talent become a singer, dancer, and actor?

Without money?

Remain frugal and unattached. Don’t take on debts, family, pet’s etc… Find a survival job in a low cost town or city with a vibrant community theater scene. When not working your survival job, contribute all your free time to a local community theater (or 2 or 3) - sell tickets, usher, work concessions, build sets, staple flyers to telephone pole, etc… Remain useful and committed (and very alert) for a long time, and learning opportunities will likely start to come your way.

Realistically, it could take several years, lots of work (and money for lessons) to be able to just land an ensemble part in a small, local community theater. You’ll need a long term view. It’s a life long process.

Best of luck!