The best way to deal with trash is to produce less of it. The next-best way is to recycle more of it, but that still leaves loads of trash. Proponents argue that burning it to produce electricity is better than burying it in a landfill.
Europe is way ahead of the US is burning trash for power. The emissions are surprisingly low and the entire process quite clean. However, it is expensive. But certainly better than dumping trash in landfills that are hundreds of miles away, like NYC does.