As to the decision itself, Scotusblog reports:

Justices, in a rare unanimous abortion ruling, agreed that the New Hampshire law could make it too hard for some ill minors to get an abortion, but at the same time they were hesitant about stepping in to fix the 2003 statute. They told a lower court to reconsider whether the entire law is unconstitutional.

....Declaring that pregnant teenagers sometimes need an immediate abortion to avert serious health problems, the Court said the New Hampshire law must be read to allow that when it occurs, which it suggested would be "in a very small percentage of cases." If the law can be interpreted to make that exception, and still be in keeping with what the state legislature intended, the Court indicated, the remainder of the law may remain intact. The state law, as written, makes an exception for teenagers where an abortion is necessary to save the pregnant girl's life, but it does not make a health exception.

The ACLU predicted the lower courts would again strike down the law. From the AP article above:

Civil rights groups predicted that the appeals court would again strike down the law. "It tells politicians that they must include protections for women's health and safety when they pass abortion laws," said Jennifer Dalven, an attorney with the American Civil Liberties Union.

By the time the case reaches the Supreme Court again, Alito will be on the bench. How would he rule?