Yes, there is a system to trash. And, after being here for two months, I am putting this system in the "good idea" column.
Trash is picked up in official trash bags of the city you live in. We purchase trash bags (gray with green writing) at our local grocery store. Trash not in these bags will not be collected.
So there it starts. You pay for the amount of trash you create. As a result, there are plenty of ways to cut back on the trash you create and save some money.
First, the Swiss are big on recycling. Two recycling centers are within walking distance for us at the Coop and Migros grocery stores. So we have officially become recyclers. No excuse when it is this easy.
Second, cardboard boxes are picked up for free. There is an area next to our dumpsters for the boxes. We just take our flattened (very important step!) boxes down there for collection.
Third, a compost bin is available for use. I'm still on the fence with this one since I'm not a big fan of flies. However, I've been told that if I use an airtight container for the compost in my kitchen, I should not get flies. We shall see, we might attempt it in the future.
Finally, everyone in Switzerland uses reusable grocery bags. Small plastic bags are available at the stores but they are pretty useless. Larger paper or plastic bags are available too but you have to pay for them. The larger bags are also designed to be able to be reused so you don't have to purchase them again. Unless, of course, you forget your bags. Which would explain the abundance of bags in our closet.
We've already seen a reduction in the trash we create by recycling, separating the cardboard boxes out, and reusing grocery bags. Good thing too, the trash bags cost a pretty penny!