If you are tired of the look of that old tile floor in your kitchen, but the thought of ripping it out and re-tiling is exhausting, there is an alternative. If the tile is structurally sound, you can paint right over it, making it any colour you choose. Because it is tile, you will need to take some extra steps to get the paint to stick. Because it is a floor, you will want to seal it in tough polyurethane. Oil-based paints are a pain to work with, but they will provide the hard, durable surface you need.
Use your belt sander and 80-grit paper to buff the surface of the tile throughout. You will not be able to sand off the surface but just dull the shine of the tile glaze and get it very clean. Vacuum up the dust.
Starting at the furthest corner of the room from the doorway, apply a coat of oil-based sealing primer with a brush. Brush it in straight, even strokes, covering the tiles and grout lines completely. Let it dry according to the instructions on the can. Generally, you will need to wait at least 24 hours for oil paint to dry.
Paint the floor with your chosen colour of floor paint, again starting from the far corner. Apply it in a thin, even layer, without trying to cover the primer completely. Let it dry. Apply a second coat and a third, if necessary.
Let the paint cure completely for at least 48 hours. Apply a coat of polyurethane gloss in the same manner as the paint, keeping it thin and even. Let it dry.
Buff the surface of the dried polyurethane with 220-grit sandpaper. Rub it by hand just enough to take the shine off the gloss.
Vacuum up the dust. Apply a second layer of gloss in the same manner. Buff and coat it again for a third layer. Let it cure for 48 hours before using the floor.
Ventilate the room when working with oil-based paints and glosses.