How best to answer a summonsfor a credit card debt?

First, your daughter must answer the summons, or she will lose right away by default (like forfeiting a ball game). Anything she can deny, she should deny; other elements, she might answer by saying that she "lacks information or knowledge as to the truth or falsity of the statement" or "lacks information sufficient to form a belief" or something similar. That won't help her down the road, if the other side can prove its case, but it buys her some time, since at least she responded. If she or you go to your state or local court website, you should be able to find instructions and possibly an template or sample for an answer.

Second, lacking the original signed contract in the summons probably does not matter, unless you believe this is not her debt and can prove its not her debt; otherwise, one way or another, when the creditor needs to, they'll prove this.

Third, she may be able to sue the ex-boyfriend for a share, if he incurred some of this debt; she may wish to speak with an attorney.

Fourth, if she simply can't afford this debt and has little income or assets potentially at stake, it may make sense for her to consider bankruptcy--it also may not, given that it's "only" $6,000, but the issue is, for her, it's an unsupportable amount. She may wish to consult with a bankruptcy attorney; filing for bankruptcy would discharge, or eliminate, the debt, though there are certainly consequences to bankruptcy, which is why it's important to consult with someone and weigh all the pros and cons.

Yes, it can be terrifying for someone to receive a summons and complaint especially when all else seems to be spiraling out of control.  She needs to take a deep breath, look at the big picture and think about a plan here.  She is lucky to have you on her side.  Now, what you are referring to is a validation of the debt, which requires that the credit card company shoe the original agreement and give a history of charges and payments when requested.  It may not be fatal to the pleading served upon her (but it is hard to tell not seeing the paperwork and really being familiar with your state law) but it can be raised when she answers.  She needs to put in an answer to the complaint by going down to court and filing one, denythe allegations in their entirety and raise affirmative defenses like she was not properly served, that the papers are defective and fail to state a cause of action, and that there is a necessary party to the litigation missing - her ex.   I am assuming that he was also on the original application.  If yes then he should be named.  Once the answer is filed she needs to seek legal help with all of this.  She needs to think about giving up the house by negotiating a deed in lieu of foreclosure and having the lender waive the deficiency.  She may want to consider bankruptcy.  She needs help.  Good luck.