First, the court found that the 2nd Amendment enumerates an individual right. Citizens have the right to keep and bear arms, and use these arms for lawful purposes, including self defense, and Federal law must recognize and respect that fact.
Second, certain types of arms are protected from bans. Which arms are protected? Reading the syllabus of the decision, one finds the following clause:
Miller’s holding that the sorts of weapons protected are those “in common use at the time” finds support in the historical tradition of prohibiting the carrying of dangerous and unusual weapons.This is an important clause in my opinion. Semi-automatic rifles to be banned in a new Federal "assault weapon" ban would include many weapons, such as the AR-15, which are "in common use at the time". In fact, the AR-15 may be the most popular rifle in the country, and getting more popular by the day, if reports from gun shops and gun shows are any indication.
Given these two facts, any new Federal "assault weapon" ban would certainly be challenged as soon as it was signed into law, and I think there would be a good chance of it being declared unconstitutional.
Heller changed everything. Gun bans are out as a tactic of gun control. They are going to have to think of something else.