If I am being sued by a credit card company, how do I ask for a continuation to seek a lawyer?

The answer to your question depends on how far along the lawsuit is in litigation.  If you are already far along in the litigation and have an upcoming court appearance, you can request a continuance from the judge to have time to find an attorney.  You might want to consider contacting Legal Aid to provide you with an attorney since you don't have any income.

If the case is not that far along where no court appearances are approaching and if you were just served with the summons and complaint (the complaint is the lawsuit attached to the summons), you will need to file an answer to the complaint within the time set forth in the summons.  If you don't timely file an answer to the complaint with the court and serve it by mail on the opposing party or the opposing party's attorney, the opposing party will get a default judgment against you.  This means you will have lost by default.  If that happens, you will need to file a motion to set aside the default.  If the court grants your motion, the case is then back on track and litigation will continue.

If the default has not been filed, you need to file the answer to the complaint.  A Legal Aid attorney can handle this for you.  If you don't have an attorney, look for answer to complaint in the index of Pleading and Practice at the law library.  This will give you the general format for an answer.  The answer to the complaint denies the allegations in the  complaint.  At the end of the answer is the verification which you sign and date under penalty of perjury.  The verification attests to the veracity of your statements in the answer to the complaint.  File the answer to the complaint with verification and an attached proof of service with the court and mail a copy to the opposing party or opposing party's attorney.  You can use a court form proof of service or you can write your own.  If you write your own, it just says that you are at least eighteen and the attached documents were sent via first class mail unless specified otherwise to ___________ (name and address of opposing party or opposing attorney) on __________ (date).  You sign and date at the bottom.  The date  you sign should be the same as the date of mailing and the same date you file your documents with the court.  The court probably charges a filing fee to file the answer to the complaint.  If you can't afford the filing fee, the court has forms you can file to waive the filing fee.

If the credit card company eventually gets a court judgment against you, you might want to consider filing bankruptcy if you can't afford to pay the judgment.  It would be premature to file bankruptcy until there is a judgment against you.