That's something that I've never done, personally and I'm not exactly sure how one would go about doing that without spending at least some money. I hope others here will be able to help you out on that one.
There is a Chinese company, or at least there was, that sold ultra thin sheets of insulation. If you can find something like that, you can uninstall it as easily as you installed it and take it with you.
Thick curtains and large area rugs may help to absorb the outside and inside noise at the same time. If those are too expensive for you, consider hanging the thick blankets you have. I find them good investments since you can use them for purposes other than soundproofing.
I have some friends with an at-home recording studio that use these foam sound panels on the walls. They don't look very nice but there's many different colors and you usually don't have to cover the entire wall. Just a part of the wall goes a long way.