How do I answer a complaint filed against me by a credit card company?

The CC debt is governed by contract law.  If the credit card is not yours and/or you did not agree to be responsible for having the benfit of the card's use/repaying the debt, then you cannot be held liable as a matter of law.  The document attached to the complaint appears to be an invoice for the amount owed.  If your position is that you are not the person on the credit card that they are suing then you need to file an answer to the complaint denying the allegations in the complaint.  You may simply file a documents that says "the defendant denies all the allegations alleges in the complaint."  You do not want a default judgment to enter which is why you need to respond.  then you need to call the lawyer representing the CC compnay and work out a deal if you are the person that owes the money or indicate you are not the person.