In some cities, trash is included with the city taxes. If so, this makes life much easier. However, if not – you would have to pay for trash. I would assume it is a flat rate, and they support recycling. Do recycle. The cost of recycling is a nominal extra, and could be fitted in with your budget.
What I Do
The apartment building I live in has a small trash chute, but with the plastic bag ban in Pittsburgh Pennsylvania, there are no such bags being provided. If you wanted those bags, you would have to buy them from places like Amazon. Instead, I use regular trash bags, and take the trash to the dumpster. I will assume that the trash collectors separates the material for recycling. Trash is included with my rent. In the city of Pittsburgh, all trash collection performed by the city will be free.