For future reference, just tell the vendor "I did not authorize this charge. Please refund me". Don't engage them further.
When that call fails (or, if they don't pick up the phone in a reasonable amount of time), call your credit card company and say "I want to issue a charge back".
They'll ask if you tried to work with the vendor. Answer "yes", full stop.
There should be a phone number associated with the charge on your credit card bill. Start (and end your interaction with the vendor) by calling that number.
Edit: You can also say "this service wasn't rendered", or "I never received the product I ordered", as applicable. Those are specifically listed as valid reasons to issue a chargeback. The person at the credit card company has to enter a numeric reason code for the charge back, and by using those phrases (or similar), you're making their lives easier.
When that call fails (or, if they don't pick up the phone in a reasonable amount of time), call your credit card company and say "I want to issue a charge back". They'll ask if you tried to work with the vendor. Answer "yes", full stop.
There should be a phone number associated with the charge on your credit card bill. Start (and end your interaction with the vendor) by calling that number.
Edit: You can also say "this service wasn't rendered", or "I never received the product I ordered", as applicable. Those are specifically listed as valid reasons to issue a chargeback. The person at the credit card company has to enter a numeric reason code for the charge back, and by using those phrases (or similar), you're making their lives easier.