This is a very practical and important question. I would say that the government can do three things.
First, the government can start an education campaign. This is not only to educate, but also to create a culture of responsibility. If the government can create this culture, then it would go a very long way.
Second, the government can give tax breaks to people who recycle. There is no greater incentive than money in our world. So, if the government can structure something like this or even if it on the town or city level, this might get people to take recycling and waste mangement a lot more seriously.
Third, the government may also want to think about fining people for not recycling. Perhaps there can be a warning and after this a fine. Again, money has a way of changing people.
the government could make you pay for your garbage to be removed from your property.