You need to be aware that each canton (and to a lesser extent each commune) will have its own trash, recycling arrangements. The federal government decided several years ago that each person was to be financially responsible for paying for the trash they produce. A few cantons, notably Geneva, are currently in an illegal situation, not having implemented these measures.
In most cantons you will find recyling centres where you can deposit recyclable items (though what is recyclable will depend on where you are) and will require the use of taxable rubbish bags for trash. Again there are plenty of ways the communes have set themselves up for taxing the bags, so you will really have to enquire locally.
The basic objective of the exercise is to incentivise people to recycle what they can and minimize the amount of trash. In the commune where I live, following the introduction of taxable bags, the amount of trash collected went down by over 40%.