One of the most obvious and most frequently overlooked solutions would be a reduction in the amount of garbage produced. Particularly in industrialized nations, packaging and other forms of waste are so common and accepted that the idea of reducing waste through more efficient packaging and consumption are foreign concepts. Yet more than any other solution, this one would be most effective.
Other methods include more significant and robust efforts at recycling, better management of waste streams to remove usable or recyclable products before they are disposed in the ocean.
Some solutions are less palatable such as increased incineration or more use of landfills as both of them still contribute to various forms of pollution and are not long-term solutions.