How do I insulate a concrete floor?

There is no need to insulate your basement concrete floor. The earth itself is the best insulator you can have, especially down lower in the ground like your basement. Water should be your primary concern and whether you have a good water barrier. Homes are designed to have the lowest part of the foundation (basement) well below the frost line, which can lift a house upward if the foundation isn't low enough, so you're in good shape insulation wise.

Unless you're in the artic I don't think it is necessary to insulate the basement floor. I've seen freezers where they insulate the floor to prevent the ground below from freezing. In those cases the insulation is installed before the floor is poured.

There is not really a need to insulate the floor if you lay carpet with padding. This will act as the insulation

You can buy a carpet pad from carpet company's that have a higher thermal barrier....it will keep the cold from wicking up through the carpet....hopefully you have a layer of plastic under the cement, to stop moisture from coming though.

there is a product available that is like osb subfloor that interlocks and has a rubber backing available called dricore. it gives the floor a warmer feeling withiut breaking uo the concrete and puttting inslab heating in.