So the only garbage processing facility I know of is the garbage dump, and it can only be upgraded with extra garbage areas and an incinerator. The incinerator creates a lot of air pollution, so is there a better alternative? I know I can plant trees, but I was wondering if there's a better way to handle garbage.
The best way to handle garbage is to start recycling!
Instead of adding to the amount of garbage needing to be collected, recycling will actually lower the amount of regular garbage to collect. As your populace becomes more and more educated, you will be collecting significanly less garbage than recycling.
Recycling is also profitable, as you can reclaim plastic, metal, and alloy by recycling. These materials fetch large prices on the world market, so when you set up your recycling center it is advised you also set up a trade depot that can accept all three of those materials. Better yet, you can start creating processors using your recycled materials and make your city high tech!
NOTE: you will never be able to eliminate regular trash completely, so the gargbage dump is still needed. A single incinerator with a single dump pile is your best option for dealing with trash. Stick your dump on the map edge, where the wind will blow the pollution out of view. Since you won't have much trash to burn, your air pollution impact will be low, and will be better than the ground pollution you'd accumulate by having lots of dumping piles. This option is also the most space efficient.
If you have the Cities of Tomorrow Expansion Pack, you will have access to the garbage atomiser. This is basically just an incinerator which does not generate pollution.