The disks are used with the felt side down if you are using them on the wood floor. I have high polish floors and if they caused any damage I would see it right away. They do not. The felt side does not scratch the floor. On the carpet they can be used with the plastic side down (the felt side down does not slide on the carpet).
An alternatives to glide disks are "Furniture Movers for Heavy Furniture", however they are slightly smaller in size. Another option is to use paper plates instead of glide disks. They are more likely to cause damage to floors with high polish, however for carpets that offer a cheap alternative. I think the the paper plates do not work quite as well as real glide disks, but it is a cheap way to see if you like this type of exercises without spending any money.
You can find it on Amazon by following this link.
Ali Julia review ★★★★★