Muslin as a curtain with the option to remove hooks
Clips and dowels
This is what I do.

You see pink broadcloth and on the on the other side is standard muslin. Zoom into the top. You’ll see clips that you can purchase at a certain furniture box store or you can use binder clips from the stationary shop with shower curtain rings from a dollar store.
In this case I used a curtain rod that I hung with command hooks to the wall so that nothing makes permanent marks and it is completely removable. It ain’t perfect or pretty but it’s been working for years and I can make it nicer when there’s time.

When I first put this up, it wasn’t stitched at all. Needed it fast. Then when I had time, did the sewing.

This is how it hangs. To tie it back, there is a shoelace pinned to it. You can be fancy and use a curtain swag. This is why there are wrinkles in the middle.
Here is another way I do this.

Nails and a dowel and string with the clips.
This piece is heavy so it hangs without help. But notice the weight stretches it.