See title. I realized that trash collection systems sometimes differ between streets... so this is just about where you live, whether it is one specific street/building or an entire country. No need to mention exactly where if you don't feel comfortable.
For where I currently live. Government makes colored trash bags (plastics/metals, papers, organic, general waste, etc) that people can buy at local supermarkets, and these bags are required for trash collection. On collection day we just... place the bags outside of the houses/apartments. Some places buy their own trash bins too, but they are rare.
The place I live in seem to take recycling very seriously. I've heard from colleagues that putting the wrong things in a bag sometimes result in the "trash police" sending a fine to where you live. Allegedly the police do that by looking at where your last letter/Amazon/random delivery address (in your paper recycling bag) was sent to...
My understanding is that it is a surprisingly effective recycling system... but with the downside that 1) the city doesn't look particularly great on/after trash collection day, and 2) sometimes the local wildlife will rip open the trash bags
Edit: some more details regarding where I live if anyone is interested. Most people only use four colored bags that are collected per week: blue (plastic, metal, something else...), yellow (paper-based recyclables), white ("residual", essentially non-recyclable items), and orange (kitchen waste). There are also bags for garden waste and heavy waste, but they are not picked up from residential addresses. Glass is either returned to the supermarket (beer bottles) or disposed of at specific dropoff bins. Things like batteries/electronics are specific, I just take them back to the store. There are also pink bags, but they are only used by businesses
Sounds a lot like Japan. There's colored bags that you can buy at the store for "combustible" and not waste. Then there's metal and glass pickup, small yard waste (mostly twigs), electronics, paper, and certain plastic has a dropoff. I've never heard of trash police issuing fines, but they'll leave your items behind if it's the wrong day or type.
When I lived in the US it was just two bins - trash (which was really anything you can fit in a bag, nobody checks) and recycling. Recycling varied by municipality but it was mostly single-stream glass, metal, and most plastics. Things like plastic bags and Styrofoam couldn't go in the recycling but most places like the grocer would take bags or fluorescent bulbs or batteries.
Of course, multiple studies have shown that most plastics just end up burned or in the ocean so guess it doesn't much matter how they are collected...