SherylM ... As you have recognized, I agree, that staples and/or thumbtacks would probably pull out too easily.
There are some permanent spray glues that would probably hold it tight.
I'm not so sure that 505 or other basting sprays would hold tight, and it might peel off on you.
I'd probably go for good ol' duct tape!
IceBlossom ... yes, go for the back of your door for a starter. Something is better than nothing!
Another forgotten about possibility are closet doors.
If you should happen to have a double door or slider ... double the space!
Another possibility is corroplast, covered with fleece (or flannelette).
Tucks in nicely behind furniture or under beds, etc. when not in use.
I started with a piece of flannelette taped to a wall with painters tape to prove the merits.
I soon upgraded to fleece on the wall .... and was totally sold.
Now ... ..... 10ft wall, floor to ceiling design wall, plus several portable ones for smaller projects.
Once you have one ... you will soon have others!