How can a 15-year-old girl and her 18-year-old boyfriend get married?

You would have to check the specific state laws. In most states parental permission is required to get married at 15. In other states they require the girl to be 16 to get married, even with permission, unless there are extenuating circumstance, such as pregnancy. All minors regardless of gender who have not been legally or conditionally emancipated need parental consent to marry. If both parents have custodial rights then both parents must sign the consent form. As previously cited, in some states a pregnant minor does not need parental permission, but she must present a letter from a licensed physician attesting to the pregnancy. If the male participant is also a minor he will need parental consent.