You must have gotten a pretty good deal...
...on the muslin, because a decent one new goes for about the same price as a decent bg stand new (say $100-$150)...
As for alternative ways to hang the thing, I guess it depends on how little you want to damage your walls. The most obvious way is to nail or tack it to the wall. Perhaps less damaging would be a low tack tape. These ways would probably be ok for something rough like a basement, utility room, or garage studio space.
If you're using a more finished space like a living, dining, or bedroom, look for existing widow treatment hardware like drappery rods or shade brackets. You might want to attach a large piece of real inexpensive cloth like unfinished muslin or drop cloth from a fabric store to the piece, and drape that part over the rod. Or place small tacks or nails in fairly hidden areas of window moulding.
Areas behind artwork on the walls also make good spots to temporarily nail or tape fabric up...