Here are the basics of the decision:
The right to keep and bear arms (RKBA) is recognized as a "fundamental right," which places it on par with freedom of speech and freedom of religion, among others. This categorization warrants "strict scrutiny" in appurtenant cases.
Strict scrutiny won't necessarily void gun registration schemes, but it will void outright bans, discretionary licensing requirements (see Scalia's discussion of "arbitrary and capricious" licensing requirements in Heller), and prohibitive taxes or licensing fees.
It should also void the Lautenberg Amendment, which extend the class of prohibited persons to those convicted of misdemeanor domestic violence crimes.
The court's recognition of the Second Amendment as protecting the RKBA especially as it relates to the right of self defense should also negate the "sporting purposes" requirement in 18 U.S.C. Sec. 922.2.
McDonald did NOT strike down Chicago's handgun ban. Rather, it remanded the case to the 7th Circuit Court of Appeals, which had previously upheld the trial court's dismissal of the case.
It's quite possible that Chicago will revise the law to bring it into what it feels is compliance with the constitution, but this fight isn't over by a long shot.
Aside from the Chicago law, others are now ripe for being challenged, including the draconian and arbitrary pistol ownership licensing schemes in places like NYC, CA, and NJ. Additionally, the assault weapons bans in NY, NJ and CA are in jeopardy.
With the Second Amendment now recognized as protecting a fundamental right, discretionary carry license laws such as those in NY, NJ, MD, and CA may also eventually be replaced with shall-issue laws.