First off, let us preface this by saying that you don't need special mats for training. :)
Any surface that is comfortable (and safe) for you to move around on is great! Carpet, gym flooring, or even grass are all good options.
But if you've got hard floors and you want to get something softer to cover them, then puzzle mats can be a great option. You can find them online or at most sporting goods stores. Order as many pieces as you need and then fit them together to make the right sized mat. If you need the space for other things (like living) then you can just pull them apart and store them out of the way after you are done.