Some youg friends received a 1099-C for cancellation of credit card debt that was done in order to avoid filing for bankruptcy. In completing their tax returns, how does one document that they were insolvent?

You will need to submit a net worth statement showing all of your debts, your assets and your income.

If the statement reflects a negative net worth, with little prospect of improvement in the near future, then the IRS will waive the taxes owed.

You need to get professional tax help to do this.