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Measure a dowel a few inches larger than your fabric width. Loop your fabric loosely over the dowel, and sew to close.
Use fish line, rope, or ribbon for hanging. Or simply set the rod on nails.
You can finish this more carefully, but when hanging from a distance, the simple seams can be sufficient, and cause less pulling.
If you'd prefer a frame, set foam batting in between the wood frame and fabric, then staple to the back. Hospital corners work well.