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
USA, Southeast. In general, you have 1 trashcan for trash and 1 recycling bin for everything that could potentially be recycled. Sometimes it's just one can for 'combined recycling' though. And if you're in an apartment, it's usually all just one big dumpster. A service comes around once a week to collect those.
If recycling is being done, the load gets dumped through an automatic waste separator (a building sized conveyor belt with machines that separate items by density). They find all the metal & recycle that. Particularly nice services will also grab the cardboard/paper. But none of them can really separate the different types of plastic from each other, so all of that goes to the landfill.
Interesting to me, the most poor/rural areas appear to be the best at recycling, as for them you must bring your trash to a transfer station yourself. And those stations have voluntary bins for each of the recycling waste streams. So if you care enough to separate your plastic into the different types (we number them 1 - 7), there's a bin for that.