How do I unclog a toilet without a plunger?

Take a wire hanger apart and use the hook end to fish out the blockage from the toilet. This isn't as effective as a plunger but it can clear up minor clogs that are relatively close to the bowl. Obviously throw away the hanger after using it. Frankly, I would suggest going to an all-night grocery or department store (several big names that I won't advertise here) and simply purchasing a plunger. It's something that always has utility and it will resolve the issue that you are experiencing the most effectively.