How can you prove your innocence if you're 19 and your age 16 girlfriend's parents kicked her out then reported her as a runaway and you got in trouble for contributing to the delinquency of a minor?

If the minor was at your place of residence or you knew where she was and failed to report it to authorities there is no defense. The only option would be to claim that you were not aware she was a runaway, however, a court would consider that a very flimsy defense argument. The best option is to obtain legal counsel as soon as possible. Most attorneys offer free or minimal fee consultation. In lieu of that choice you may have to enter a Nolo Contendre plea to receive a reduced sentence agreement. The final dispensation of the matter will depend upon state laws and how aggressively the PA wishes to pursue the case.