If you mean a trash can for an apartment, condo, or small office, the easiest ones are usually the simplest designs. In my experience, one-piece molded plastic cans with a snap-on lid are the fastest to set up—open the box, pop the lid on, and you are basically done. Rubbermaid Commercial Slim Jim-style bins are a good example because they arrive ready to use and do not need tools.
For kitchen step cans, look for models that come preassembled except for the lid or pedal. Some steel pedal bins from brands like Simplehuman and Brabantia are sturdy and fairly easy, but a few require you to align the lid and insert a hinge pin. That is still simple, just not as instant as a snap-fit plastic bin.
I would avoid flashy sensor bins and dual-compartment recycling cans if assembly speed is your top priority. They often have more parts—inner buckets, liner rings, battery compartments, and sensor lids—and the instructions can be fussy.
If you actually mean public urban trash cans, the easiest are usually single-piece rotationally molded bins or concrete-and-steel receptacles that arrive fully assembled. The catch is that they are heavy and may need bolting down, not assembly.
My short answer: choose a one-piece molded plastic urban trash can with a snap-on lid, or a preassembled pedal bin with only one or two parts to attach. Check reviews for phrases like “no tools required” and “ready out of the box,” and skip anything with more than a few screws or a sensor.