Paper plates work well on carpets.
And rags work well on wood floors, as do socks (large socks over the top of your shoes, for example).
On carpet, you can also use Gliding Discs (round, like the discs Cathe and crew are using) or furniture movers (the big, rectangular ones), or "Valslides" (which are basically just the big, rectangular furniture movers, but in green and about 3x the price, LOL!).
If you're on puzzle mats, the best solution is to put down a small rug or bath mat and use the options that work on carpet.