Supporting the floor on a raised framework will give added flexibility and may save you the hassle of tearing out the existing floor.
Lay 1-by-2-inch lumber in rows every 12 to 16 inches to lift your flooring up. This can be laid over any level surface, including tile and carpet.
Extra dense closed cell foam, known as PVA, can be cut into square blocks and tacked with staples to the underside of your 1-by-2-inch lumber for extra give.
An even cheaper option is to use several layers of carpet pad to support the 1-by-2-inch lumber. This will not last as long and does not give as much bounce, but is cheaper and easier to find.
There are several inexpensive options for the actual floor panels. Choose something that can easily be nailed or screwed to your 1-by-2-inch lumber to give the floor stability. For a quick, temporary floor, plywood panels can be laid flat on top of the existing floor to give a better surface.
Panels of ½-inch to ¾-inch plywood make a great floor. Many houses have plywood underlayment beneath their floors. Plywood can be painted, or sanded and sealed with non-skid poly or wax finishes.
Particle board or medium-density fiber core are also good options. While MDF is typically a little more expensive than plywood, particle board is cheaper, but may not last as long. Either of these can be sealed or painted, or used in conjunction with hardboard paneling, such as masonite.
Hard-board panels are very durable. They are sold in 1/8-inch and ¼-inch thicknesses and can be used alone, with gaffer's or duct tape to joint the seams, or as the top layer of a built-up floor. They can be sealed or painted.
Different styles of dance require different qualities of your floor. Consult the instructors to make sure the floor you are installing will meet their needs.
Rubberized floors, often called marley, can be purchased in rolls and added to built-up floors or rolled out alone to serve as temporary flooring. These can be purchased from dance and theatrical suppliers. These are typically used in classical, soft shoe, styles such as ballet, jazz and modern.
Wood surfaces, such as parquet or plywood provide, work well for practicing tap and ballroom. Properly built up to give enough flex, they can also work well for classical styles.
Paint is by far the cheapest option. Semigloss latex can make a suitable dance surface if your budget is the main concern. Repaint it often as the build of paint on the surface will give your floor a more desirable texture. Dark colors such as brown and black will show less wear.