If the floor has existing ceramic or vinyl flooring, you can choose to either install new tiles directly on top; remove the old flooring before tiling; or, in the case of vinyl, install backerboard directly on top and then install the tiles. Whichever option you choose, make sure the floor is strong enough.
Resilient tiles or sheet flooring: Old resilient floorings include vinyl, linoleum, asphalt, and asbestos. If a single layer of non-cushioned resilient flooring is firmly attached, you can install ceramic or stone tile directly on top; for vinyl with a shiny surface, rough up the vinyl with a sanding block first.
Where there is more than one layer of resilient flooring, or where the flooring is cushioned, remove the flooring. If a stiff scraper does not do the job, use a flat prybar and a hammer. An iron can help soften the adhesive.
Lay a cloth on top of the tiles, turn the iron to the highest setting, and iron the cloth, keeping the iron moving. After ten seconds or so, try prying up on the tile. If the adhesive is still not soft, repeat the process.
Ceramic tile: You can install new ceramic or stone tile directly on top of firmly attached ceramic or stone tile. If the old tile is glazed, rough up the surface using a belt sander, a tile stone, or a grinder to ensure that the thinset will adhere. When the existing surface has deep grout lines, you can probably set large tiles on top with no problem, but small tiles may be uneven.
Experiment first by laying down the new tiles without adhesive; if they form an uneven surface, fill the old grout lines with thinset, allowing it to dry before starting to tile. Removing ceramic tile can be difficult, especially if the tiles are set in an old-fashioned mortar bed. A cold chisel and hammer are usually the most efficient tools.
More about tile flooring preparation and installation:

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