How would a minor whose parent has been using her name on delinquent accounts for years go about getting a free credit report?

The Fair Credit Reporting Act 15 USC 1681c-1 Section 605 A (2) reads "Access to free reports. In any case in which a consumer reporting agency includes a FRAUD ALERT in the file of a consumer...the consumer reporting agency shall (A) disclose...that the consumer may request a free copy of the file..."

So, you need to contact the credit bureaus and follow their procedures for getting a fraud alert placed on your file. Once there, you are allowed under law to request your free reports.

This may be accomplished by means of contacting the Federal Trade Commission and following their instructions for victims of identity theft. These actions often lead to a police report for the crime. I've taked with many people who did not want to go to the police when the perpetrator is a family member. This is often one of the first steps to protecting yourself and re-establishing your rights under law.